Latihan Fisika

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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439

Q1. The dimension of permeability is

(a) ML2T

−2A

−1 (b) ML

2T

−2A

−2 (c) MLT

−2A

−1 (d) MLT

−3A

−1

Q2. In which of the following pairs, the two physical quantities do not have the same dimensional formula

(a) pressure and stress (b) impulse and momentum

(c) work and energy (d) moment of inertia and angular momentum

Q3. Dimensions of young’s modulus and shear modulus are

(a) different (b) same, and are that of work

(c) same, and are that of force (d) same, and are that of pressure

Q4. The dimension of co−efficient of viscosity is

(a) ML−1

T−1

(b) M0L

−1T

−2 (c) ML

2T

−1 (d) MLT

2

Q5. Given the dimension of potential difference ML2T

−3A

−1. The dimension of resistance is

(a) MLT−3

A−2

(b) ML2T

−3A

−2 (c) ML

2T

−3A

−1 (d) ML

2T

−3A

−3

Q6. The dimension of Planck’s constant is

(a) it is dimensionless, since it is a constant (b) same as that of frequency

(c) ML2T

−1 (d) ML

2T

−2

Q7. The period of oscillation, T of a floating cylinder with length h immersed in a liquid of density ρ is, T = 2π c

hρ,

where c is a constant. The dimension of C is

(a) it is dimensionless (b) MLT−2

(c) ML−2

T−2

(d) L2T

−2

Q8. Which one of the following is not a base SI unit

(a) coulomb (b) kilogram (c) metre (d) candela

Q9. The speed of a particle varies in time according to v = AT − Bt3. The dimensions of A and B respectively are

(a) L, LT−2

(b) L, LT−3

(c) LT−2

, LT−4

(d) L2, LT

−4

Q10. In the equation (V − b) 2

ap RT

v

+ =

, where v is the volume, P is the pressure, T is the absolute temperature and R

is the universal gas constant, the constants a and b have the dimensions

(a) M2L

4T

-2 θ, L

4 (b) ML

5T

−2 θ, L

3 (c) ML

5T

−2 θ, L

3 (d) ML

5T

−2, L

3

Q11. The speed v of a particle of mass m as a function of time t is given by v = αA

1/ 2

sink

tm

, where dimension of A

is L. The dimensions of α and k respectively are

(a) LT−1

, MLT−2

(b) T−1

, MT−2

(c) LT−2

, MLT−2

(d) LT−2

, ML−1

T−2

Q12. If A and B have different dimensions, which one of the following operations is not possible.

(a) AB (b) 1 − A/B (c) A − B (d) AB1/2

Q13. Let Q is the length of an object found by taking two readings (a and b) using a ruler of least count 0.1 cm. Let a = 16.4

cm and b = 25.3 cm. Q should be written as

(a) 8.9 ± 0.2 cm (b) 8.9 ± 0.1 cm (c) 8.9 (d) none of these

Q14. The radius of a circle is 10 ± 0.2 cm. The percentage error in its area is

(a) 2% (b) 12.56% (c) 4% (d) 1%

Q15. In an experiment, the thickness of a wire was measured at 4 points with a micrometer with least count ± 0.01 mm. 4

readings are 0.67 mm, 0.65 mm, 0.63 mm, 0.64 mm The thickness should be quoted as

(a) 0.6475 m (b) 0.648 ± 0.012 mm (c) 0.6 ± 0.01 mm (d) 0.65 ± 0.01 mm

Q16. In a vernier calipers the least count of main scale is 0.05 cm. 50 divisions of vernier scale coincide with 49 divisions of

main scale. The least count of vernier scale is

(a) 0.1 mm (b) 0.01 mm (c) 0.01 cm (d) 0.05 mm

Q17. The following parameters have been measured for a particle moving in a circular path, velocity = 20 ± 1 ms−1

, radius =

10±0.1 m, mass = 5 ± 0.5 kg. The force on the particle is

(a) 200 ± 42 N (b) 200 ± 32 N (c) 200 ± 0.21 N (d) 200 ± 21 N

Q18. The planck’s constant has the same dimension as

(a) angular velocity (b) energy (c) angular momentum (d) momentum

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Q19. The quantity eh/(4πm) has the same dimension as

(a) electric dipole moment (b) magnetic dipole moment

(c) potential difference (d) current density

Q20. Which one of these is dimensionless

(a) refractive index (b) resistivity

(c) universal constant of gravitation (d) solar constant

Q21. The product of resistance and capacitance has the same dimension as

(a) permittivity (b) potential difference (c) magnetic flux (d) time

Q22. The equation of motion of a rocket is

v - V0 log ,vM

t1 0

0

+

α− where v is the velocity of the rocket at time t, v0 in its initial velocity, M0 is its initial mass

V0 is the velocity of the fuel ejecting out of the vehicle with respect to the vehicle. The constant α has the dimension

(a) it is dimensionless (b) M (c) T (d) MT−1

Q23. In the graph shown, five points are plotted along with

their errors. While fitting a straight line minimum

weight should be taken for the point

Y

A

BC

DE

X

(a) A (b) B (c) C (d) D

Q24. In the graph shown the readings of current in a resistor

versus the potential difference across the resistor are

plotted, which one of the following statement is

definitely wrong.

(a) there is no backlash error in ammeter and

voltmeter

(b) variation of current with voltage is linear

(c) the ammeter has least count of 0, 1 A

(d) the voltmeter has least count of 0.1 V

i

V

1A

1 2 3 4

Q25. SI unit of amount of substance is

(a) kg mole (b) g mole (c) amu (d) mole

Answers

1. (c) using the formula of force between two current carrying conductors Force/unit length = r

II

2

210

π

µ

2. (d) 3. (d) 4. (a)

5. (b): obtain it from v = iR

6. (c) 7. (c) dimension of two sides of equation must be equal

8. (a): 9. (c) same as 7

10. (d): a/v2 has dimension of P and b has dimension of V

11. (b): the argument of a trigonometric function must be dimensionless

12. (c) 13. (a): ∵ ∆Q = ∆a + ∆b

14. (c): if Q = c xn the

X

xn

Q

Q ∆=

∆ [c const]

15. (d): average of all reading ± ( )∑ − readingsof.no/readingeachaverage .

16. (b) 17.(a): ∆F/F = ∆m/m + 2∆v/v + ∆r/r 18. (c) 19.(b) 20. (a)

21. (d) 22. (d) 23. (c) 24. (a) 25.(d)

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Q1. To describe the motion of bodies these are generally considered size as point objects. For this which of the statements is

true

(a) the laws of motion are valid only for truly point size objects

(b) the laws of motion are valid for all bodies which move distance much larger than their own sizes

(c) the laws of motion are valid for all bodies irrespective of their sizes and the distance they move

(d) the laws of motion are valid for large bodies even if they move distance much less than their sizes

Q2. Which of the following in a closest example of motion in one dimension

(a) a train moving on a railway track

(b) a boat sailing on a lake over distances small compared to earth radius

(c) a billiard ball in motion

(d) earth moving around the see

Q3. The position-time graph for an object is shown below.

This is an example of

(a) motion in one dimension

(b) motion in two dimensions

(c) motion in three dimensions

(d) stationary object

x

x0

True

Q4. Which of the graphs (velocity-time) represents uniform motion

(a)

velocity (v)

time(t) (b)

(v)

(t) (c)

(v)

(t) (d)

(v)

(t)

Q5. A body is uniform motion in one dimension moves from a position x at time t to another position at time t′. Which of

the statements is wrong for this motion.

(a) the actual distance covered in time t to t′ is the magnitude of displacement

(b) the velocity calculated by making any choices for t and t′ always gives the same result

(c) a larger value of the difference t′ − t will give a small value of the velocity because velocity is obtained by dividing

by t′ − t

(d) a larger value of x′ − x will give larger value of the velocity.

Q6. For a body in uniform motion in one dimension, which of the following statements is not true

(a) the body has constant speed

(b) the body has constant velocity

(c) the body has constant acceleration

(d) the body moves equal distance in equal time intervals.

Q7. Which of the graphs (position−time) represents uniform motion in one dimension

(a)

position

(x)

time (t) (b)

x

t

(c)

x

t (d)

x

t

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Q8. For uniform motion in one dimension which f the statements is not true

(a) both speed and velocity can be positive

(b) both speed and velocity can be negative

(c) velocity can be either positive or negative but speed is always positive

(d) both speed and velocity can be zero

Q9. Which of the following graphs describing the uniform motion of two bodies (1) and (2) represents zero relative velocity

between them.

(a)

Position x

time (t)

(2)

(1)

(b)

x

t

(2)

(1)

(c)

x

t

(2)(1)

(d)

x

t

(2)

(1)

Q10. Which of the following does not represents motion with constant acceleration

(a) time (t)

velocity v

(b) time

velocity

(c) time

velocity

(d) time

velocity

Q11. The figure below describing the motion of a body in one

dimension state which statement is not true

(a) segment AB and EF represents motion with uniform velocity

(b) segment BC represents motion with positive acceleration

(c) segment CD represents motion with constant acceleration

(d) segment DE represents motion with negative acceleration A

1

A2

AB

C

D

E F

Time

Position

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Q12. Which of the following curves describes motion with positive constant acceleration.

(a) time (t)

velocity v

(b) t

v

(c) t

v

(d) t

v

Q13. Which of the following represents motion with negative constant acceleration motion

(a) time (t)

velocity v

(b) t

v

(c) t

v

(d) t

v

Q14. Which of the following does not represent a constant acceleration motion

(a) time (t)

velocity

v

(b) time (t)

velocity v

(c) time

velocity

(d) time

velocity

Q15. A car accelerates on a straight road from rest to a speed of 50 m/s in 25 sec. The distance covered by car in this time is

(a) 1250 m (b) 625 m (c) 2 m (d) 1/2 m

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Q16. Two trains move with speeds 100 km/hr on parallel trades opposite to each other. Which statement is true

(a) The relative velocity between trains is 200 km/hr

(b) The relative velocity between train is zero

(c) The relative velocity between trains is 100 km/hr

(d) The velocity of earth relative to both trains is same

Q17. In the displacement−time graph below the ratio of

speeds during the first two seconds and the next four

seconds i

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) 3 : 2

time1 2 3 4 5 6

5

10

25displacement

20

Q18. For the velocity−time graph below what is the ratio of

the distance covered by the body in the last two

seconds of its motion to the total distance covered

(a) 2 : 3

(b) 1 : 2

(c) 1 : 3

(d) 1 : 4

1 2 3 4 5 6 7

5

10

15

20

velocity

time (s)

Q19. The variation of the speed of a car with time is given

as

The maximum acceleration is in the segment

Speed

Time

A

B

C

D

E

(a) AB (b) BC (c) CD (d) DE

Q20. A car accelerate from rest at constant rate α for sometime after which it decelerate at constant rate β to come to rest. If

the total time of motion is t, the maximum velocity acquired by the car is

(a) αβ/α + β (b) α + β/αβ (c) α2 + β2

/(αβ) t (d) α2 − β2

/(αβ) t

Q21. A train moves from rest to rest for time t, accelerating at constant rate a α for sometime and then decelerating at

constant rate β for the remaining time. The distance covered is

(a) tβ+α

αβ (b)

2t11

β+

α (c)

2t2

1

αβ

β+α (d)

2t

2

1

β+α

αβ

Q22. When a particle is in motion, its

(a) average speed is equal to the magnitude of its average velocity

(b) average velocity can never be zero

(c) average speed can never be zero

(d) average velocity is always half he sum of initial and final velocity

Q23. Two trains are heading towards each other on the same track with velocity v1 and v2 respectively. The drivers, noticing

this when the trains are at a distance � apart, apply brakes, giving same acceleration α to each train. The necessary

condition for no collision is

(a) ( )

�<α

+

4

vv2

21 (b) �<α

+

4

vv 22

21 (c) �<

α

+

2

vv 22

21 (d)

( )�<

α

+

8

vv2

21

Q24. Which of the following is not a vector quantity

(a) displacement (b) speed (c) velocity (d) acceleration

Q25. A body falls from rest under gravity. The distance moved by it during the 2nd

second is

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(a) 1/2 g (b) g (c) 3/2 g (d) 2g

Q26. The velocity of a body which has fallen freely under gravity through a height h is given as gp h

q. p, q are given by

(a) p = 1, q = 1 (b) p = 1 q = 1/2 (c) p = 1/2 q = 1/2 (d) p = 1/2 q = 1

Q27. The velocity time graph of a body is shown in the

figure. The acceleration of the body

(a) decreases with time

(b) is uniform

(c) increases with time

(d) decreases in the beginning and the starts increases

v

t

Q28. A wooden block, starting from rest, slides down are inclined plane of length L with an acceleration a0 and reaches the

bottom with a speed of 10 m/s. If the length of the plane were 2L, it would reach the bottom with a speed.

(a) 5 m/s (b) 10 m/s

(c) 14 m/s (d) depending upon the angle of inclination

Q29. A body moving with an initial velocity v covers a distance of 15 m in the sixth second and 19 m in the eighth second. It

has an acceleration

(a) zero (b) 1 m/s2

(c) 2 m/s2 (d) which can be determined only if v is known

Q30. A body starting from rest has a velocity 2 ms−1

when it has covered a distance 2m. Its velocity after covering a distance

20 m is

(a) 10 m/s (b) 20 m/s (c) 10√2 m/s (d) 2√10 m/s

Q31. A body when released from certain height reaches ground in 40. The time taken to cover half the distance is

(a) √2 sec (b) 2√2 sec (c) 4√2 sec (d) 2 + √2 sec

Q32. A body released form the roof of a building 10 m high takes time t to hit the ground. It will take twice as much time if it

is dropped from a height of

(a) 14 m (b) 20 m (c) 28 m (d) 40 m

Q33. The linear speed of the seconds hand of a wall clock is 1.05 cm s−1

. The length of the seconds hand is nearly

(a) 1 cm (b) 5 cm (c) 10 cm (d) 60 cm

Q34. The velocity−time graph of a body is shown. The

distance covered by the body two seconds after start is

(a) 8 m

(b) 12 m

(c) 16 m

(d) 20 m

9 m/s

5 m/s

v

4s t

Q35. A body under uniformly acceleration motion covers 20 m in first second and another 40 m in the 2nd

second. The initial

velocity of the body is

(a) zero (b) 5 m/sec (c) 10 m/sec (d) 20 m/sec

Q36. A ball thrown vertically upwards reaches a maximum height of 20 m and falls back to the thrower. It will reach time

after (g = 10 m/s2)

(a) 2 sec (b) 4 sec (c) 8 sec (d) 16 sec

Q37. The distance−time graph of the motion of a body is

given below. It represents the body

(a) in uniform motion

(b) thrown vertically upwards

(c) released from the top of a tower

(d) none of the above

s

t

Q38. The acceleration of a particle starting from rest varies with time according to the relation a = kt + c, k and c being

constants. The velocity of the body after time t will be

(a) kt2 + ct (b) ctkt

2

1 2 + (c) ct2

1kt

2 + (d) 22

ct2

1kt

2

1+

Q39. A body freely falling from a tower of height h covers a distance h/2 in last second of its motion. The height of the tower

is (g = 10 ms−2

) nearly

(a) 50 m (b) 55 m (c) 58 m (d) 60 m

Page 6


Q40. For a particle moving with a constant speed along a straight line AB, the hodograph will be

(a) a straight line parallel to AB (b) a straight line perpendicular to AB

(c) a circle with diameter along AB (d) first a point

Answers

1. (b)

2. (a)

3. (d): position remains constant with time

4. (a): velocity remains constant with time

5. (c): displacement will also be large if time interval is large

6. (c): acceleration will change the velocity

7. (a)

8. (b): speed can not be negative; negative speed is meaningless

9. (a): ∆x is constant for equal ∆Ts; equal slopes of the st. line.

10. (b)

11. (a): AB represents stationary state so does EF

12. (b): velocity increases uniformly

13. (c): velocity decreases uniformly

14. (c) slope is not constant

15. (b): Acc. = 50/25 ms−2

; s = 1/(2) at2

16. (c)

17. (c): in inverse to time intervals

18. (d): in proportion to the areas under the respective curves.

19. (c): CD is the steepest portion − maximum slope

20. (a): αt1 − β(t − t1) = 0 and v = αt1

21. (d): as in Q20 (a)

22. (c): speed is always taken to be +ve

23. (c): use s = ut − 1/(2) at2, s ≤ �

24. (b)

25. (c): s1 = 1/(2) g, s2 = 1/(2) g . 22

26. (c)

27. (a): at t increase slope decrease

28. (c): v2 − u

2 = 2as

29. (c): s = ut + 1/(2) at2

30. (d) θ2 − u

2 2as, v = u + at

31. (b): s = ut + 1/(2) t2

32. (d): as above

33. (c): in 60 sec the second travel a distance 2π �

34. (b)

35. (c): s = ut + 1/(2) at2

36. (b): as above

37. (c): s = 1/(2) at2 a parabola

38. (b): direct integration gives the result

39. (c): s = ut + 1/(2) at2, v

2 − a

2 = 2as

40. (d): def. of hodograph.


Q41. In uniform circular motion of a body

(a) the speed is constant but velocity changes

(b) both speed and velocity change

(c) the speed change but velocity is constant

(d) both speed and velocity are constant

Q42. In uniform circular motion which of the following does not remain constant

(a) speed (b) velocity (c) acceleration (d) angular displacement

Q43. For a particle moving in a circular path with uniform speed, when the acceleration is along Y axis, the velocity will be

along

(a) X−axis (b) Y−axis (c) (−X) − axis (d) (−Y) − axis

Q44. Which of the following is true for a particle moving in a circle with a uniform speed

(a) acceleration is zero (b) acceleration is parallel to velocity

(c) acceleration is antiparallel to velocity (d) acceleration is perpendicular to velocity

Q45. If the instantaneous acceleration and velocity are at right angles to each other and are both non zero, during the motion

(a) velocity (b) does not change with time

(c) both velocity and speed do not change with time (d) both velocity and speed change with time

Q46. The angular speed of a geostationary satellite is nearly

(a) π rad/h (b) π/12 rad/h (c) π/24 rad/h (d) π/720 rad/h

Q47. Two satellites are orbiting earth at distances, respectively, 7,000 km and 42,000 km from its centre. Their centripetal

accelerations will be in the ratio

(a) 6 : 1 (b) 1 : 6 (c) 36 : 1 (d) 1 : 36

Q48. Two satellites of names m1 and m2 (m1 > m2) are revolving around the earth in circular orbits of radii r1 and r2 (r1 > r2).

Which of the following statements about their velocity is true

(a) v1 = v2 (b) v1 < v2 (c) v1 > v2 (d) v1/r1 = v2/r2

Q49. The ratio of angular speed of earth around sun to the angular speed around its own axis is nearly

(a) 365 (b) 1/365 (c) 1/24 (d) 1/12

Q50. All points on a rotating disc have same

(a) angular velocity (b) linear velocity

(c) linear velocity and angular velocity (d) none of the above

Q51. The angle between the vectors A = a1x + b1y + c1z and B = − a1x − b1y − c1z is

(a) zero and their magnitudes are equal (b) 90° and their magnitudes are equal

(c) 180° and their magnitudes are equal (d) 180° and their magnitudes are unequal

Q52. The angle θ between the vector A = y2x + and its positive direction of x−axis is given by

(a) sinθ = 1/2 (b) cos θ = 1/2 (c) sin θ = √1/5 (d) cos θ = √1/5

Q53. Which of the following statements about vectors is false

(a) The magnitude of a vector is always a scalar

(b) Each component of a vector is always a scalar

(c) Two vectors in a plane can add to give a null vector

(d) Three vectors not lying in a plane can never add up to give a null vector.

Q54. If 0dcba =+++�

�

�

�

, which of the statements is not true.

(a) dandc,b,a�

�

�

�

must each be a null vector

(b) magnitude of ( )ca��

+ equals magnitude of ( )db��

+

(c) the magnitude of a�

can never be greater than the sum of magnitudes of dandc,b�

�

�

(d) ( )cb�

�

+ must lie in the plane a and d if a and d are not collinear and in the line of danda�

�

if they are collinear.

Q55. Which of the following statements about vectors is not true

(a) two vectors having different magnitudes can not be combined to give zero resultant

(b) minimum three vectors all of different magnitude are required to give resultant null vectors

(c) a vector can not have zero magnitude if one of its components is non zero

(d) sum of magnitudes of two vectors can never be equal to magnitude of the same of these two vectors

Q56. Which of the following statements about vectors C,B,A��

are false


(a) B.A��

= 0 means that A�

and B�

are necessarily perpendicular to each other

(b) If C.AB.A��

= , it follows CB��

=

(c) If ,0BA =×��

A is parallel to B or anti parallel to B

(d) If ,CBA =×��

C is a perpendicular to the plane containing A�

and B�

Q57. If ,0B.A =��

then BA��

× is

(a) zero (b) AB (c) AB (d) (AB)2

Q58. Given A = k2j3i4 −+ and k4j6i8B −+=�

the angle between A & B is

(a) 90° (b) 60° (c) 45° (d) 0°

Q59. If ,CBA =×��

then C is

(a) normal to both A & B (b) normal to A only

(c) normal to B only (d) neither normal to A nor to B

Q60. Which of the following is false

(a) If three vectors add upto zero, they all must be in the same plane

(b) The magnitude of difference between two vectors can be greater than magnitude of either vector

(c) The magnitude of difference between two vectors can never be greater than the magnitude of the same of the two

vectors

(d) three non coplanar vectors can never add upto null vector.

Q61. A vector R�

in the first quadrant is given by R ≡ a sinθ i + acosθ j . Then the vector ;R perpendicular to R in the

second quadrant is

(a) − a cosθ i + a sinθ j (b) a cosθ i + a sinθ j

(c) a cosθ i − a sinθ j (d) − a cosθ i − a sinθ j

Q62. A vector R�

in the first quadrant is given by R ≡ a sinθ i + acosθ j . The vector ;R perpendicular to R in the 4th

quadrant is

(a) − a cosθ i + a sinθ j (b) a cosθ i + a sinθ j

(c) a cosθ i − a sinθ j (d) − a cosθ i − a sinθ j

Q63. If A�

is any vector and n a unit vector in its direction, then we can write

(a) n/|A|A��

= (b) n/A|A|��

= (c) |A|nA��

= (d) |A|An��

=

Q64. For a particle executing uniform circular motion

(a) velocity is radial, acceleration is radial (b) velocity is transverse, acceleration is radial

(c) velocity is transverse, acceleration is transverse (d) velocity is radial, acceleration is transverse

Q65. In the following graphs to represent the motion of a body in a fixed frame in a given direction, which cannot be

observed in nature.

(a) displacement

time

(b) time

velocity

(c)

time

speed (d)

displacement

Time


Q66. A car moves on a square track, ABCD of side 1000 m. Considering its motion from A to C which takes place in 50

second, its average speed is (m/sec).

(a) 40 (b) 20√2 (c) 80 (d) 20

Q67. In the above question, the average velocity of the car is

(a) 20 (b) 20√2 (c) 40 (d) 80

Q68. A body projected with velocity u at an angle α from a point P on a horizontal plane strikes the plane at Q. The average

velocity of the body for the journey P to Q is

(a) 1/2 u cosα (b) u/2 (c) u cosα (d) u sinα

Q69. Two particles of mass m1 and m2 more along concentric circular paths of radii r1 and r2 respectively and complete are

revolution in the same time. The ratio of their angular velocities is

(a) m1 : m2 (b) r1 : r2 (c) m1r1 : m2r2 (d) 1 : 1

Q70. A body projected with velocity u attains a horizontal range of u2/2g. The angle of projection is

(a) 15° (b) 30° (c) 45° (d) 60°

Q71. Two stones are thrown simultaneously from the same point with an initial velocity 20 ms−1

, one straight up and other at

an angle of 80° to the horizontal. The distance between the stones after 2 seconds is

(a) 40sin180 − (b) ( )80sin1240 − (c) ( )80cos80sin240 − (d) 40cos180 −

Q72. A particle moves in XY plane with the velocity jbxiaV +=�

where a and b are constants. The path of the particle is

(a) always a parabola (b) a parabola if a ≠ 0, b ≠ 0

(c) a straight line if a = 0, b ≠ 0 (d) always a circle

Q73. Two particles are projected horizontally from the same elevated point in opposite directions with velocity 4 m/s and

9 m/s respectively. At the moment when their velocity vectors are mutually perpendicular, the separation between then

is (g = 10 m/sec2)

(a) 2.5 m horizontally (b) 24.7 at an angle tan−1

(9/4) to the horizontal

(c) 7.8 m horizontally (d) 2.5 m at angle tan−1


Q74. A particle is projected from a point O with velocity u at angle θ (upward) to the horizontal. At a certain points P it is

moving at right angles to its initial direction which of the statement is not true

(a) The time of flight form O to P is u/g sinα (b) OP makes an angle tan−1


(c) The velocity of the particle at P is u cotα (d) The distance of P from O is 1/2g (u/sinα)2

Q75. A car travel certain distance at a speed of 40 km/hr and then returns the same distance at a speed of 10 km/hr. The

average speed for the whole journey

(a) is 16 km/hr (b) is 20 km/hr (c) 425 km/hr (d) can not be determined

unless the distance is known.

Q76. One of the rectangular components of a velocity of 50 m/s is 30 m/s. The other component is

(a) 15 m/sec (b) 20 m/sec (c) 25 m/sec (d) 40 m/sec

Q77. A man drives 10 km north and then 20 km to the east. This displacement from the starting point is approximately

(a) 10 km (b) 20 km (c) 22 km (d) 30 km

Q78. Which of the following sets of displacements be capable of returning a car to its starting point

(a) 5, 10, 30 and 50 km (b) 50, 50, 50 and 250 km (c) 15, 30, 50 and 100 km (d) 4, 6, 8, and 15 km

Q79. A body starts from rest and moves with constant acceleration of 10 m/s2 in the first 10 second. During the next 10

seconds it moves with the uniform velocity attained. The total distance covered by the body is

(a) 500 m (b) 1000 m (c) 1500 m (d) 2000 m

Q80. If a body in motion covers distances in direct proportion to the square of the time elapsed, it is moving with acceleration

which is

(a) zero (b) constant (c) increasing (d) decreasing

Q81. A body starts moving from rest under the influence of constant acceleration. If covers a distance x in first two second

and a distance y in the next two seconds, then

(a) y = x (b) y = 3x (c) y = 2x (d) y = 4x

Q82. A hunter aims at a monkey hanging from a tree branch. Just at the instant he fires at it, the monkey drops. Which of the

following statements is true.

(a) the bullet with hit the monkey (b) the bullet will pass above the monkey

(c) the bullet will pass below the monkey (d) the data is not sufficient to predict anything


Q83. A particle is projected from a point O with a velocity u in a direction making an α upward with the horizontal. At P,

when it is moving at right angles to its initial direction of projection, its velocity at P is given by

(a) u tanα (b) u cotα (c) u cosecα (d) u secα

Q84. In the above question (Q83), the time of flight from O to P is

(a) g

eccosu α (b)

g

sinu α (c)

g

tanu α (d)

g

secu α

Q85. A projectile from O must hit a target at P such that OP is 120 m while the vertical height of P above the horizontal plane

through O is 60 m. The initial velocity of projection in m/s at O must not be less than

(a) 42 (b) 50 (b) 72 (d) 80

Q86. In the above question (Q85) the direction of projection from O for minimum velocity to hit P must make with horizontal

an angle

(a) 45° (b) 53° (c) 60° (d) 75°

Q87. A boy aims a gun at a target at a horizontal distance 100 m. If the gun can impart a velocity of 500 ms−1

to the bullet at

which height above the target must he aims his gun in order to hit it. (g = 10 ms−2

)

(a) 20 cm (b) 10 cm (c) 50 cm (d) 100 cm

Q88. From the top of a tower 40 m height a ball is projected upwards with a speed of 20 m/s at an angle of elevation of 30°.

The ratio of total time taken by the ball to hit the ground to the tune taken to come back to the same elevation is

(g = 10 ms−2

)

(a) 2 : 1 (b) 3 : 1 (c) 3 : 2 (d) 4 : 1

Q89. The horizontal displacement, from the foot of the tower, of the ball in the above question (Q88) is nearly

(a) 50 (b) 60 (c) 70 m (d) 80 m

Q90. A cannon on a level plane is aimed at an angle α above the horizontal and a shell is fired with muzzle velocity v0

towards a vertical cliff a distance R away. Then the height from the bottom at which the shell strikes the side wall of the

cliff is

(a) R sinα α

−22

0

2

sinv

gR

2

1 (b) R cosα

α−

220

2

cosv

gR

2

1

(c) R tanα α

−22

0

2

cosv

gR

2

1 (d) R tanα

α−

220

2

sinv

gR

2

1

Q91. The coordinates of a moving particle at any time t are given by x = ct2 and y = bt

2. The speed of the particle is given by

(a) 2t (c + b) (b) 2t 22

bc + (c) 22

bc + (d) ( )22 bct2 −

Q92. The acceleration of the particle in the above question (Q91) is

(a) 2 (c + b) (b) 22

bct2 + (c) 22

bc2 + (d) 22

bct2 −

Q93. The equation for the path of the particle in above question (Q91)is

(a) y2 = 4bc x (b) 1

y

y

c

x2

2

2

2

=+ (c) xc

by = (d) 1

b

y

c

x2

2

2

2

=−

Q94. A body thrown from a height in a horizontal direction comes down

(a) vertically with uniform velocity (b) vertically with uniform acceleration

(c) along a curved path with uniform velocity (d) along a curved path with uniform acceleration

Q95. The path of a body thrown from a height in a horizontal direction with a given velocity u is

(a) straight line (b) hyperbola

(c) parabola (d) any curve depending upon the velocity u

Q96. At what angle to the horizontal should a bullet be fired to attain maximum horizontal range.

(a) 30° (b) 60° (c) 45° (d) 90°

Q97. At what angle to the horizontal should a ball be thrown to attain maximum vertical range

(a) 30° (b) 60° (c) 45° (d) 90°

Q98. A bird flying with speed of 50 km/h enters the compartment of a train running in the same direction at a speed of 60

km/hr through an open window. The bird

(a) will hit the rear wall of the compartment

(b) will hit the front wall of the compartment

(c) will remain at the position of the window it entered


(d) will hit the wall opposite to window at a point directly opposite to it

Q99. A car moves along a straight horizontal road with a speed (i) v and (ii) 3 v. Assuming identical conditions, the ratio of

the shortest distance in which the car canbe stopped is

(a) 1 : 3 (b) 1 : 27 (c) 1 : 9 (d) 1 : 81

Q100. The horizontal range of a projectile released with an initial speed u at angle of projection θ is given by

(a) u2/g (b) u

2/g sin 2θ (c) u

2/2g (d) u

2/g sinθ

Answers

41. (a)

42. (b)

43. (a): accl is radial inwards, particle is at the bottom moving right

44. (d)

45. (b): accl has no component in the direction of velocity

46. (b): geostationary satellite has same ang. Speed as earth

47. (c): a = v2/R

48. (b): F = mv2/r

49. (b)

50. (a)

51. (c): vectors are mirror images of each other

52. (d): cosθ = x x′ + yy′ / 2222 'y'x.yx ++

53. (b): component can be either +ve or − negative

54. (a)

55. (d): statement is true of vectors are along the same line

56. (a): is true of one of A or B is null vector

57. (b): A . B = AB cosθ, AxB > AB sinθ, θ = 90°

58. (d): cosθ = 4 × 8 + 3 × 6 + ( −2) (4) / (42 + 3

2 + 2

2)

1/2 (8

2 + 6

2 + 4

2)

1/2 = 1

59. (a): def of cross product

60. (c)

61. (a): draw components

62. (c): as above

63. (c): definition

64. (b)

65. (a): time cannot decrease

66. (a): addition of equal scalars 1 to each other

67. (b): addition of equal magnitude vectors 1 to each other

68. (c): linear velocity horizontal is u cosα

69 (d): definites

70. (a): 0 = u sinθ − gt, u2/2g = ucosθ × t × 2

71. (c): as above s = ut + (1/2) gt2

72. (b): vx = (dx/dt) = ia , vx = (dy/dt) = bx j ⇒ x, y

73. (c): at that moment velocities in original direction are zero.

74. (d): as above (g cos α) t = u cotα etc.

75. (a): av. Speed is total distance moved divided by total time.

78. (d)

79. (c): s = ut + (1/2) at2

80. (b): as above

81. (c)

82. (a)


83. (b)

84. (a) as above

85. (a) as above

86. (c)

87. (a)

88. (a) v2 − u

2 = 2as, v = u + at

89. (c)

90. (c) s = ut + (1/2) at2, v = u + at

91. (c): v2 = vx

2 + vy

2 ; vx = dx/dt, vy = dy/dt

92. (b): a = (dv/dt)

93. (b) eliminate t

94. (d)

95. (b)

96. (b)

97. (d)

98. (a): relative velocity

99. (b): the desired ratio is proportion to the ratio of its square of the velocity.

100. (c)


Q101. Newton−sec is the unit of

(a) energy (b) force (c) angular momentum (d) momentum

Q102. A stretching force of 5N is applied at one end of a spring balance and an equal force is applied at the other end in the

opposite direction. The reading in the balance will be

(a) zero (b) 5N (c) 10N (d) 15N

Q103. A person weighing 80 kg is standing on a life which is moving upwards with a uniform acceleration of 4.9 m/sec2. The

apparent weight of the person will be

(a) 40 kg (b) 80 kg (c) 120 kg (d) 160 kg

Q104. A jet engine works on the principle of conservation of

(a) man (b) energy (c) linear momentum (d) angular momentum

Q105. A 10 kg weight is accelerated from rest to 50 m/s. The force acting on it

(a) 410

× 50 N (b) 410

× 05 × 9.8 N

(c) N50102

14

2×× (d) cannot be determined from the give data

Q106. A charge of mass 10 kg is fired from a cannon of 20 kg with a speed of 100 m/sec. The velocity of recoil of the cannon

is

(a) 100 m/sec (b) 50 m/sec (c) 200 m/sec (d) 10 m/sec

Q107. A man in a lift will weigh more when the left

(a) begins to go up (b) is going up steadily (c) is coming down steadily (d) is slowing down

Q108. An iron ball and a wooden ball of the same radius are released from a given height in vacuum. Which of the following

statements is the

(a) Iron ball will reach the ground fast (b) Wooden ball will reach the ground fast

(c) both balls will reach the ground at the same (d) no ball can reach the ground

Q109. The correct answer to the above question is based upon the fact that

(a) acceleration due to gravity in vacuum depends upon the mass f the body

(b) there is n acceleration due to gravity in vacuum

(c) the acceleration due to gravity has the same value irrespective of the mass of the body

(d) the motion of bodies is not possible in vacuum

Q110. O being slightly displaced, if the distance between the center of gravity of the body and the ground remains unchanged,

the body is

(a) in stable equilibrium (b) in neutral equilibrium (c) in unstable equilibrium (d) not in equilibrium a all

Q111. If a railway train is moving with a uniform speed on a level track, the engine is doing

(a) no work (b) work against friction

(c) work against gravity (d) work against both friction and gravity

Q112. Balanced on a wedge at a point 5 cm from one end, a metre scale remains horizontal when a mass of 180 g is

suspended from the same end. The weight of the metre scale is

(a) 20 g (b) 36 g (c) 90 g (d) 180 g

Q113. A object placed on ground in stable equilibrium is given a slight push. The initial position of its centre of gravity

(a) moves nearer to ground (b) rises higher above the ground

(c) remains unchanged (d) does not have anything to do with the type of equilibrium

Q114. A false balance has unequal areas of length a and b. If W1 and W2 are the balancing weights, when a body is weighed

alternately in the two pairs the true weight of the body is given by

(a) 21WW (b) 22

1 WW + (c) W1 + W2/2 (d) W1W2/W1W2

Q115. The ratio of the arms of the balance in the above question a/b is

(a) W1/W2 (b) 21 W/W (c) W12 + W2

2 (d) W1W2/W1 + W2

Q116. A bullet hits and gets embedded in a solid block resting on a frictionless surface. In this process

(a) momentum is conserved

(b) kinetic energy is conserved

(c) both momentum and kinetic energy are conserved

(d) neither momentum nor kinetic energy is conserved

Q117. A ball of mass 0.1 kg, thrown against a wall normally with a velocity 30 m/s. rebounds with a velocity of 20 m/sec in

the opposite direction. The impulse of the force by the ball on the wall is


(a) 50 N−S (b) 0.5 N−S (c) 1 N−S (d) 5 N−S

Q118. A body slides down an inclined plane of inclination θ. The coefficient of friction down the plane varies in direct

proportion to the distance moved down the plane (= kx). The body will move down the plane with acceleration which is

(a) constant g sinθ (b) constant (g sinθ − µg cosθ)

(c) constant (µ g cosθ − g sinθ) (d) variable which goes to zero then become negative

Q119. Three different objects of mass m1, m2, m3 are allowed to roll from rest along three different frictionless paths OA, OB,

OC. The speeds of the three objects on reaching the ground will be in the ratio

(a) m1 : m2 : m3 (b) 1 : 1 : 1 (c) m1 OA : m2 OB : m3 OC (d) OA/m1 : OB/m2 : OC/m3

Q120. A ball is moving to and fro about the lowest point of a smooth hemispherical bowl. If is able to rise upto a height of 45

cm. on either side, its speed at the lowest point must be (g = 10 m/s2)

(a) 4.5 m/s (b) 9 m/s (c) 3 m/s (d) 0.045 m/s

Q121. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at free

end of the rope, the force exerted by the rope on the block will be

(a) Pm/M + m (b) Pm /M + m (c) Pm/M − m (d) P

Q122. In the arrangement shown below, masses M1 and M2 are both descending with uniform speed v. The mass M will

ascend with speed

θ θ

M1 M

2

M

(a) v cosθ (b) 2v cosθ (c) 2v/cosθ (d) v/cosθ

Q123. A container, filled with water, and having a wooden block floating in it is allowed to fall freely under gravity. During

the fall, the upthrust on the wooden block will be

(a) equal to the weight of the block is air

(b) equal to the weight of the block is water

(c) equal to the weight of the water displaced by the block

(d) zero

Q124. Two identical frictionless pulleys are arranged separately as

shown. Assuming that strings have negligible mass, the

acceleration of mass m in the two cases will be

(a) same but different from g

(b) same and equal to g

(c) more in case (1) than in case (2)

(d) more in case (2) than in case (1)

m

m

2m

F = 2mg

(1) (2)

Q125. A man is pulling on a rope attached to a block on a smooth horizontal table. The tension in the rope will be same at all

the points

(a) if and only if the rope is not accelerated (b) if and only if the rope is massless

(c) if either the rope is massless or not accelerated (d) always

Q126. A spring balance A and a beam balance B are used to weigh given object at different points on the earth. Then

(a) The readings A and B will be different on different points

(b) The readings of A will be different but those of B will be same

(c) The readings of A will be same but those of B will be different

(d) both A and B will have the same readings

Q127. A plum lie is hanging from the ceiling of a car. When the car is moving along the horizontal track with an acceleration

a, the plumy line gets inclined at an angle


(a) tan−1

(a/g) (b) tan−1

(g/a) (c) cos−1

(a/g) (d) sin−1

(g/a)

Q128. A black slides on a smooth inclined θ kept on the floor of a lift when the lift is descending with a retardation a, the

acceleration of the block relative to the incline is

(a) (g − a)sinθ (b) (g + a) sinθ (c) g sinθ (d) (g − a)

Q129. An object takes n times as much longer to slide down a 45° rough incline as it takes to slide down a perfectly smooth

45° inline. The coefficient of kinetic friction between the object and incline is

(a) µk = 2n1

1

− (b) µk =

2n1

1

− (c) µk =

2n

11− (d) µk =

2n

11−

Q130. Two blocks of mass 3 kg and 2 kg are attached to the ends of a string passing over a smooth pulley fixed to the ceiling

of an elevator. A man inside the elevator find the acceleration of the system to be g/4. The acceleration of the elevator is

(a) g/4 downwards (b) g/4 upwards (c) g/20 downward (d) g/20 upward

Q131. A smooth sphere A moving in a straight line collides elastically with an identical stationery sphere B. The spheres

move in different directions after the collisions. The angle between the directions of motion of the spheres after the

collision

(a) will be larger if the velocity of A is more (b) is independent of the magnitude of velocity of A

(c) depends upon the angle at which A hits B (d) will always be right angle

Q132. Two blocks A (1 kg) and B (3 kg) rest one over the other on a

smooth horizontal plane. The coefficient of static and dynamic

friction between A & B is same and is equal to 0.75. The

maximum horizontal force in Newton that can be applied to A

in order that both A and B donot have relative motion is

1 kg

3 kg

A

B

F

(a) 2 × 9.8 (b) 14.7 (c) 9.8 (d) 4.9

Q133. In the question above if the horizontal force F is applied to B (in place of A), its maximum value in Newton when there

is no relative motion between A & B is

(a) 3 × 9.8 (b) 2 × 9.8 (c) 1 × 9.8 (d) 0.49

Q134. A particle of mass 0.1 kg is released from rest from the vertex

of a wedge of mass 2.5 kg which is free to slide on a frictionless

horizontal plane. The particle slides down the smooth face AB

of the wedge. When the velocity of the wedge is 0.2 m/sec, the

velocity of the particle relative to wedge is

(a) 4.8 m/sec

(b) 5 m/sec

(c) 7.5 m/sec

(d) 10 m/sec

A

m = 0.1 kg

M = 2. 4kg

v

B

60

2 m/sec

Q135. The result of two equal forces acting a point perpendicular to each other is

(a) equal to either of the force (b) equal to √2 time one of the forces

(c) equal to twice of the either force (d) zero

Q136. The angles which the result wakes with either of the forces in the above question is

(a) are equal and of magnitude 45° (b) are equal and of magnitude 90°

(c) are equal and of magnitude 60° (d) are not equal

Q137. Two equal forces acting at a point give a resultant equal to either of them. The angle between the force is

(a) 0° (b) 60° (c) 90° (d) 120°

Q138. The angle which the resultant in above question makes with either of the forces is

(a) 30° (b) 45° (c) 60° (d) 90°

Q139. A man weighing 75 kg stands in an elevator. The force exerted by him on the floor of the elevator will be zero when

(a) the elevator goes up at a uniform speed (b) the elevator goes down at a uniform speed

(c) the cable of the elevator breaks and it falls freely (d) the elevator goes up at an acceleration of 9.8 m/sec2

Q140. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle.

If the motion of the particle takes place in a plane, it follows that

(a) its velocity is constant (b) its acceleration is not constant

(c) its momentum is constant (d) it moves in a circular path

Q141. If a body is in unstable equilibrium, on being slightly displaced, its centre of mass and potential energy will

(a) rise, decrease (b) rise, increase (c) be lowered, increase (d) be lowered decrease


Q142. A particle of mass m collides with another of same mass such that the coefficient of restitution is 1. After the collision

the particle will move

(a) opposite to each other (b) parallel to each other

(c) perpendicular to each other (d) at an angle of 45° to each other

Q143. An object of mass 2 kg starts from rest and moves along X−axis under the action of a Force F = (5 + 3x) N when it has

tavelled a distance of 2m, nearly.

(a) its velocity is 4 m/sec (b) its acceleration is 4m/sec2

(c) its motion is simple harmonic (d) all the above statements are wrong

Q144. M1 (= 2 kg) rests on a frictionless surface while the coefficient

of friction between M1 and M2 (1 kg) is 0.2. If a force of 1.5 N

is applied on the mass M1 as shown.

(a) The system will move with an acceleration of 0.5 m/sec2

(b) M2 will remain stationery on M1

(c) The masses will move with an acceleration 0.75 m/sec2

(d) M2 will remain stationary while M1 slips under it

M = 1 kg2

M = 2 kg1

1.5 N

Q145. If the force acting on a body is doubled as also the mass of the body, the acceleration of the body

(a) reduces to half its value (b) remains unchanged

(c) becomes double of its earlier value (d) becomes four times its earlier value

Q146. A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall with the same

velocity bounces back. It is because

(a) the initial momentum of the metal ball is greater

(b) metal ball suffers a greater change in momentum

(c) rubber ball suffers a greater change in momentum

(d) initial momentum of rubber ball is greater

Q147. Which of the following statements is true

(a) a body moving in circle with constant speed has no acceleration

(b) the tension in a cable supporting a lift remains constant irrespective of its motion

(c) the inertia of a body is the resistance offered by it to change its motion

(d) whenever an action is produced by a force on a body, there is an equal and opposite reaction on the same body

Q148. A block of mass 6 kg rests on a rough inclined plane of angle 30° and co−efficient of friction 2/3. The frictional force

on the block is

(a) 3 × 9.8 N (b) 2/√3 × 9.8 N (c) 2 × √3 × 9.8 N (d) 4 × 9.8 × N

Q149. Two particles of equal masses are attached one to the end A

and other to the mid point B of a string. The other end of the

string is fixed to a point O. The particles describe concentric

circles with O as centre in a smooth horizontal plane such that

O, B and A are always collinear. The ration of the tension T1 &

T2 is

T1

B T2

A

(a) 1 : 2 (b) 4 : 1 (c) 3 : 2 (d) 2 : 1

Q150. A body of weight 50 N is pushed with just enough force to start it moving across a floor and the same force continues

to act afterward. Coefficients of static and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is

(a) 1/10 g (b) 5.6 g (c) 0.56 g (d) 1/5.6 g

Q151. A motor of mass 150 kg moves with a retardation of 2m/s2 round a curve of radius 100 m. When the speed of the

motion is 15 m/s, the total exerted by the vehicle on the road is

(a) 3375 N (b) 1470 N (c) 1528 N (d) 337.5 N

Q152. Two block A (1 kg) and B (3 kg) rest on a smooth

horizontal surface as shown. The coefficient of friction

between the blocks is 3/4. The maximum horizontal

force F, that can be applied to A so that A and B do not

have relative motion is

1 kg

3 kg

A

B

F

(a) 14.7 N (b) 9.8 N (c) 19.6 N (d) 4.9 N


Q153. A chain of length � rests on a rough horizontal table with one end hanging over the table edge. The chain just starts to

slide down on its own when the overhanging length equals 4/� . The coefficient of friction between the chain and the

table is

(a) 3/4 (b) 2/3 (c) 1/4 (d) 1/3

Q154. Two bodies of unequal mass m1 and m2 are attached to the ends of a string passing over a light smooth fixed pulley.

The force exerted by the pulley on its support is

(a) < (m1 + m2) g (b) (m1 + m2) g (c) > (m1 + m2) g (d) zero

Q155. A coin rests on a gramophone record at a distance r from its centre. The coefficient of friction between the coin and the

record surface is µ. The record starts revolving and attains an angular velocity ω, the coin still remaining on it. It

follows that

(a) ω ≤ (µg/r)2 (b) ω ≤ grµ (c) ω ≤

r

gµ (d) ω ≤

r

gµ

Q156. Figure below shown the position−time graph of a

particle of mass 4 kg. Which of the statements abut the

force F acting on the particle is not true

(a) F = 0 for t < 0

(b) F = 0 for 0 < t < 4

(c) F = 0 for t > 4

(d) F ≠ 0 for t > 6 O 4 6 t(s)

A B

C

3

X(m)

Q157. In the problem above (Q156) which of the following statements about the impulse is false

(a) Impulse a t = 0 is zero

(b) Impulse at t = 0 is 3 kg m/sec

(c) Impulse at t = 4 is equal and opposite to the impulse at t = 0

(d) Impulse between 4 ≤ t ≤ 6 is not zero

Q158. A monkey of mass 40 kg climbs on a rope which can stand a maximum tension of 600 V. In which of the following

cases will the rope break. The monkey (g = 10 ms−2

)

(a) climbs up with an acceleration 6 ms−2

(b) climbs down with acceleration 4 ms−2

(c) climbs up with uniform speed of 5ms−1 (d) falls down the rope nearly freely under gravity

Q159. For an ordinary terrestrial experiment which of the observer is inertial frame

(a) a child revolving in a giant wheel with constant speed

(b) a sports man is a sports car with a constant

(c) a pilot of an aeroplane during take off

(d) the guard of a train slowing down on a platform

Q160. The correct sequence of fundamental forces of nature in increasing order of their strength is

(a) strong , electromagnetic, weak, electromagnetic

(b) electromagnetic, strong, weak, gravitation

(c) gravitation, weak, electromagnetic, strong

(d) weak, electromagnetic, strong, gravitation

Answers 101. (d)

102. (b)

103. (c): a′ = a + g

104. (c)

105. (d): accl. Should be known

106. (b): conservation of momentum

107. (a): as in Q103

108. (c): g is same for both

109. (c)

110. (b): definition

111. (b)

112. (a): taken moments about Co.



114. (a): take moments

115. (b): as above

116. (c)

117. (d)

118. (d): kinetic friction acts opposite to velocity and proportional to it


120. (c)

121. (a): definition

122. (b): tension is same on each

123. (d): free fall no acceleration

124. (d) definition

125. (c)

126. (b): I varies on surface of earth so spring balance will be effected

127. (a): vector addition of two acceleration

128. (b): as above

129. (c)

130. (a): accl. Balanced in stationery life

131. (d)

132. (c)

133. (a)

134. (d): conservation of momentum

135. (b): vector addition of forces

136. (a): as above

137. (d):

138. (c):

139. (c): case of free fall−weightlessness

140. (d): characteristic of uniform circular motion

141. (d): definition

142. (c): definition

143. (a): F = ma, v2 − u

2 = 2as


145. (b): definition F = ma

146. (c):

147. (c): definition


149. (c)


151. (b)

152. (c)


154. (a)

155. (d) definition

156. (b): Force with cause displacement of body

157. (a): Impulse is change in momentum at an instant

158. (a): calculate T in storng

159. (b): uniform motion is inertial frame

160. (c): In order of increasing strength gravitation < weak < electromagnetic < strong.


Q221. A shell fired from a gun at an angle to the horizontal explodes in mid air. The centre of mass of the shell fragments will

have

(a) vertically down

(b) horizontally

(c) along the same parabolic path of the unexploded shell

(d) along the tangent to the parabolic path of unexploded shell

Q222. The centre of mass of a system of two particles is

(a) on the line joining then and midway between them

(b) on the line joining them at a point whose distance from each particle is proportional to the square of the mass f the

particle

(c) on the line joining them and at a point whose distance from each particle is proportional inversely to the mass of

that particle

(d) on the line joining them and at a point whose distance from each particle is proportional to the mass of that particle

Q223. Of the two spheres of same size, mass and appearance one is hollow and other is solid. If the two are rolled down an

inclined plane simultaneously, then

(a) hollow sphere will reach the bottom first

(b) solid sphere will reach the bottom first

(c) both will reach bottom together

(d) either can reach first depending upon the surface of the plane

Q224. A loaded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation θ. The gun is initially

at rest on a horizontal frictionless surface. After firing, the centre of mass of the gunshot system

(a) moves with a velocity vm/M

(b) moves wit a velocity vm/M cosθ in the horizontal direction

(c) remains at rest

(d) moves with a velocity ( )

( )mM

mMv

−

− in the horizontal direction

Q225. If a mass of mass M jumps to the ground from a height h and his centre of mass moves a distance x in the time taken by

him to hit the ground, the average force acting on him (assuming constant retardation) is

(a) Mgh/x (b) Mgx/h (c) Mg(h/x)2 (d) Mg(x/h)

2

Q226. The motion of the centre of mass of a system of two particles is unaffected by their interval forces

(a) only if these are along the line joining the particles

(b) only if there are at right angles to the line joining the particles

(c) only if there are obliquely inclined to the line joining the particle

(d) irrespective of the actual direction of the interval forces

Q227. The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis is

(a) 1 : 2 (b) 5 : 6 (c) 2 : 3 (d) 2 : 1

Q228. A massive circular hoop of radius r oscillates in its own plane about a horizontal axis at a distance x above the centre of

the hoop. The period of oscillation is minimum, when x equals

(a) r (b) r/2 (c) r/3 (d) zero

Q229. A jet engine works on the principle of conservation of

(a) mass (b) energy (c) linear momentum (d) Angular momentum

Q230. A rectangular container half full of petrole is being carried by a train on a horizontal track. If the train accelerates, the

surface of the petrole in the container with respect to horizontal surface will

(a) be raised upward from the front (b) be raised in the middle

(c) be raised upward from the back (d) remain unchanged

Q231. A rod of length L revolves with angular velocity ω about an axis through its centre and perpendicular to its length. If A

is the area of cross−section of the rod and d its density, then its kinetic energy will be

(a) dA3

1 23ω� (b) dA2

1 23ω� (c) dA2

1 22ω� (d) dA3

1 22ω�

Q232. A particle moves in a circle with uniform speed. When its goes from pt A to diametrically opposite point B, its

momentum changes by Aa PP��

− = 2 kg m/s j and the centripetal force acting on it changes by AB AF��

− = 8N i . The

angular velocity of the particle is


(a) 4 radian/s (b) 16 radian/s (c) 2/π rad/sec (d) dependent upon its mass

Q233. For the particle in the above problem (Q232), if the displacement in 1/4th

of the time period is 0.3 m, the radius of the

circle is nearly

(a) 0.11 m (b) 1.2/√2 m (c) 0.15 m (d) 0.6/π m

Q234. A sphere and right circular cylinder have both same mass and radius. The moment of inertia (MI) of sphere about its

diameter

(a) more than MI of cylinder about its axis

(b) equal to MI of cylinder about its axis

(c) les than MI of cylinder abut its axis

(d) can be more or less than MI of cylinder about its axis depending upon the length of the cylinder

Q235. If both the sphere and cylinder (question no. 234) roll down the same incline sphere will reach bottom

(a) earlier than cylinder (b) later than cylinder

(c) at the same time as cylinder (d) earlier or later depending upon the surface

Q236.

Q237.

Q238. Two identical uniform rods P and Q move

with same velocity v as shown in the figure.

The rod Q has aG additional angular velocity ω

(< 6v/ � ) clockwise abut G′

A A′B B′

G

v v

G′

P

(a) If ends A and A′ are suddenly fixed simultaneously both rods with rotate with the same angular velocity

(b) If ends A and A′ are fixed simultaneously, the rod Q will rotate with greater angular velocity

(c) If the ends B and B′ are suddenly fixed both rod will rotate with same angular velocity

(d) If the ends B and B′ are fixed simultaneously the rod will rotate greater angular velocity

Q239. A uniform circular disc placed on a rough horizontal surface has initially a linear velocity v0 and an angular velocity

w0. If the disc comes to rest after moving some distance in the direction of motion, then v0/rω0 is

(a) 1/2 (b) 1 (c) 3/2 (d) 2

Q240. A solid right circular cylinder is placed on a rough plane of inclination α to the horizontal. The coefficient of friction

between the cylinder and the plane so that the cylinder rolls down (without sliding) is

(a) tan α (b) sin α (c) 1/3 tanα (d) 3/2 tanα

Q241. A uniform rod AB of mass in length � at rest on a smooth horizontal surface is subject to an impulse P at the end B.

The time taken by the rod of turn through a right angle is

(a) 2πm 1/p (b) 2π p/m � (c) πm � /12 p (d) π p/m �

Q242. A particle moves along an arc of a circle of radius R. Its velocity depends upon the distance covered as v = a√S, a

being a constant. The angle α between the total acceleration vector and velocity vector is given by

(a) tanα = √2 S/R (b) sinα = S/R (c) sinα R

S2 (d) tanα = (2S/R)

Q243. A mass m on a frictionless table is attached to a hanging mass M by a chord through a hole in the tale surface. The

angular velocity with which the mass in must rotate on a circle of radius r such that mass M may hang in equilibrium at

rest is

(a) mr

Mg (b)

Mr

mg (c)

r

g

M

m1

+ (d)

r

g

Mm

Mm

+

Q244. The trajectory of a ‘fixed’ point on the rain of a wheel of a vehicle as the vehicle moves with a constant speed is being

observed by an observer fixed on ground. The trajectory, as noted by him will be

(a) a circle coinciding with circumference of the wheel repeating itself

(b) a parabola with vertex at the highest point on the wheel

(c) a straight line parallel to road

(d) a cycloid, repeating itself with every rotation of the wheel

Q245. One end of a light inextensible string is fixed to a point on a smooth horizontal table. A mass 3m is tied to the other

extremity and a mass m is tied at the mid point of the string. Both the masses remain on the table with string straight and

taut. The mass are now so projected on the table that they revolve in circles with uniform sped about the fixed end of string

such that the two parts of string remains in straight line. The ratio of the tensions in the two parts of the string is given by


(a) 1 : 2 (b) 1 : 3 (c) 3 : 2 (d) 6 : 7

Q246. A particle of mass m is placed inside a hemispherical bowl of radius 10√2 m. rotating about its vertical axis with

constant angular velocity ω. The particle is just prevented from sliding down when the radius vector OP joining it to the

centre of the bowl makes an angle of 45º with the axis. If the coefficient of friction between the particle and the bowl is

0.5, the value fo ω (given g = 10 ms−2

) is

(a) √2 rad/s (b) 1/√3 rad/s (c) √3 rad/sec (d) 1/√3 rad/sec

Q247. A wheel of mass 4M in the form of a disc of radius r is accelerated from rest about a fixed axis through the centre by a

constant tangential force of magnitude Mg for 10 sec. The angular speed of the wheel at the end of 10 sec will be

(a) g/r rad/sec (b) 5r/g rad/sec (c) 4g/r rad/sec (d) 5g/r rad/sec

Q248. The rotor of a helicopter has 4 blades, each of length 2m and making 10 rev/second. A tip of one of the blades

weighing 1 kg is lost in an accident. The resultant sideways force on the helicopter is approximately

(a) 100 N (b) 2000 N (c) 5000 N (d) 8000 N

Q249. Three garden rollers have the same diameter and total mass. The roller A has most of the mass concentrated on rain.

The roller B has the mass concentrated near the axle while the roller C is uniform solid cylinder. If the rollers are listed

in order according to the case with which they may be accelerated, it will be

(a) ABC (b) ACB (c) BAC (d) BCA

Q250. The moment of inertia plays the same role in rotational motion as is played in linear motion by

(a) velocity (b) momentum (c) energy (d) mass

Q251. The driving wheel of a belt drive attached to an electric motor has a diameter of 38 cm and operates at 1200 ?. The

tension in the belt is 130 N on the slack side and 600 N on the tight side. The power transmitted tote wheel by the belt is

(a) 5 kw (b) 7.5 kw (b) 10.6 kw (d) 11.2 kw

Q252. The human body can withstand an acceleration a times that due to gravity. The minimum radius of curvature with

which a plot may safely turn a plane vertically ? at the end of a dive when the planes speed is 770 km/hrs.

(a) 519 m (b) 612 m (c) 475 m (d) 323 m

Q253. At time t, a particle of mass m has position vector r = r cosθ i + r sinθ j . If the angular momentum of the particle

about the origin C k all the time, C being a constant, the value of φ is

(a) φ =mr

Ct (b) φ =

2mr

Ct (c) φ =

C

tmr 2

(d) φ = 2

2

Cr

mt

Q254. A particle moves in a circle of radius 4 cm. clockwise at constant

speed 2cm/sec. If x and y are unit accelerations vectors along x

and y respectively (in cm s−2

), the accelerates of the particle half

way between P & Q is given by

P

y

Qx

O

(a) − 4 ( )yx + (b) 4 ( )yx + (c) ( ) 2/yx +− (d) ( ) 4/yx + s

Q255. If ω is the angular velocity vector for earths rotation and R and V are position and velocity vectors for a particle

irrespectively in earths reference frame, then carioles acceleration is given by

(a) ω × (ω × R) (b) ω × v (c) 2v × ω (d) v × ω

Q256. A student sitting on a pivoted stool holds the axle of a bicycle vertical. Holding the stool, the wheel is set into spinning,

with angular momentum L0 upwards. Now the stool is released and the student suddenly turns the axle upside down by

180°. As a result the student and stool will start spinning with angular momentum

(a) L0 upwards (b) 2L0 upwards (c) 2L0 downwards (d) L0 downwards

Q257. A symmetrical wheel radius 12 cm is mounted on its axis kept horizontal. A light cord is wrapped round the wheel and

supports a 0.40 Kg mass. If this is released from rest, with the string taut, the object is observed to fall with acceleration

3ms−2

. Given g = 10 ms−2

, the moment of inertia of wheel about its axis is nearest to (Kg m2)

(a) 0.0135 (b) 0.0192 (c) 1.35 (d) 192

Q258. A closed tube, partly filed with a liquid and set horizontal is rotated about a vertical axis passing through its centre. In

the process the momentum of inertia of the system about its axis would

(a) increase always

(b) decrease always


(c) remain constant

(d) increase if the tube is less than half filled, decrease otherwise

Q259. A uniform rigid rod has length L and mass m. It lies on a horizontal smooth surface and is rotated at a uniform angular

velocity ω about a vertical axis passing through one of its ends. The force exerted by the axle on the rod will be

(a) mω2L outwards (b) mω2

L inwards (c) 1/2 mω2L outwards (d) 1/2 mω2

L inwards

Q260. A wheel is rolling straight on ground without slipping.

If the axis of the wheel has speed v, the instantaneous

velocity of a point P on the rim defined by angle θ

relative to ground will be

θ

P

(a) v cos (θ/2) (b) 2v cos (θ/2) (c) v (1 + sinθ) (d) v (1 + cosθ)

Q261. A uniform ring of radius r and mass per unit length P is spun about its axis with an angular velocity ω. The increase in

tension due to stretching of the ? is proportional to

(a) ρr2 ω2

(b) ρrω2 (c) ρr

2ω (d) ρ1/2 r

2ω2

Q262. A wheel of radius 40 cm. rolls over a plane with angular velocity 10Hz without slipping. Which of the following

statements is true ?

(a) The speed of its centre of mass is 8 ms−1

(b) The speed of its point of contact with the plane is zero

(c) The velocities at the ends of horizontal diameter are equal

(d) Velocity at the upper end of vertical diameter is 4 ms−1

horizontally

Q263. A particle of mass m is executing uniform circular motion abut affixed axis with speed v. If r�

and F�

are radius vector

and centripetal force respectively, the value of torque is

(a) zero (b) positive non zero constant

(c) negative non zero constant (d) variable

Q264. The angular momentum for the above particle (Q 264) is

(a) zero (b) mv/r (c) mvr (d) infinity

Q265. The areal velocity for the above particle (Q 264)is

(a) zero (b) 1/2 (dr/dt)2 (c) rω (d) 1/2 vr

Q266. For a particle rotating about a fixed axis with non−uniform angular velocity, there

(a) is only radial acceleration

(b) is only tangential acceleration

(c) is neither radial nor tangential acceleration

(d) are both radial acceleration and tangential acceleration

Q267. A particle moves in the XY plane in a circular path with constant velocity about the z − axis in clockwise direction. For

this particle

(a) angular momentum and torque point in the same direction

(b) angular momentum and linear momentum point in the same direction

(c) angular momentum and angular velocity are in the same direction

(d) angular momentum and linear velocity are in the same direction.

Q268. A particle moves in the X−Y plane about the Z−axis

in the anticlockwise direction with uniform velocity.

The direction of the angular velocity is along

(a) X−axis

(b) Y−axis

(c) + Z−axis

(d) − Z−axis

Z

Y

X

Q269. A rigid body rotates abut a fixed axis by the application of a force. For this body

(a) the direction of angular momentum is along the direction of torque

(b) The direction of change of angular momentum is along the direction of torque

(c) the direction of angular momentum is along the direction of force

(d) the direction of change of angular momentum is along the direction of force.

Q270. If the total external force acting on a rigid body is zero, then

(a) only linear momentum remains constant


(b) only angular momentum remains constant

(c) both linear momentum and angular momentum remains constant

(d) neither linear momentum nor angular momentum remain constant

Q271. The moment of inertia of a plane circular disc (Mass M radius R) about an axis passing through its centre and

perpendicular to its plane is (1/2 MR2). The momentum of inertia about one of its diameters will be

(a) 1/4 MR2 (b) 1/2 MR

2 (c) MR

2 (d) √2 MR

2

Q272. Three bodies of same mass are rotating about a

symmetrical axis passing through each as shown with

the same angular speed. Then

ω ω ω

M

MM

I1 I

2

I3

(a) I1 = I2 = I3 (b) I1 > I2 > I3 (c) I1 < I2 < I3 (d) none of the above

Q273. A hollow cylinder and a solid cylinder both having same mass and same radius are rotating abut their axis with the

same constant angular speed. Then moment of inertia of solid cylinder

(a) will always be more than that of hollow cylinder

(b) will always be equal to that of hollow cylinder

(c) will always be less than that of hollow cylinder

(d) will be equal, less or more than that of hollow cylinder depending upon the speed of rotation

Q274. One end of a string of length � is connected to a particle of mass m and the other to a small peg on a smooth horizontal

table. If the particle moves in a circle with speed v, the net force on the particle is (T ≡ tension in the string)

(a) T directed towards the centre (b) T − e

mv 2

directed towards centre

(c) T + e

mv 2

directed away from centre (d) zero

Q275. A stone of mass m is tied to a string of length � is whirled round in a horizontal plane in a circle of radius r. The speed

of the stone is increased beyond the maximum permissible value and the string breaks suddenly; then

(a) the stone will jerk radially outwards

(b) the stone will jerk radially inwards

(c) the stone will fly off tangentially from the instant the string breaks

(d) the stone flies off at an angle α, such that tanα is proportional to the speed of the stone

Q276. Which of the following statements is false

(a) During rolling the force of friction acts in the same direction as the direction of motion of the centre of mass of the

body

(b) The instantaneous speed of the point of contact during rolling is zero

(c) The instantaneous acceleration of the point of contact during rolling is zero

(d) For perfect rolling, work done against friction is zero

Q277. The moment of inertia of a thin uniform rod of mass M and length � about an axis passing through its centre and

perpendicular to its length is ML2/12. The momentum of inertia about a parallel axes through its end is

(a) M �2/12 (b) M �

2/6 (c) M �

2/3 (d) M �

2/2

Q278. Which of the statements about the momentum of inertia of a body is true

(a) Moment of inertia of a body is always constant independent of the axis about which it rotate

(b) Moment of inertia of a body depends upon the speed with which it rotate

(c) Moment of inertia of a body about an axis passing through its centre of mass is zero

(d) Moment of inertia of a body depends upon the distribution of mass in the body

Q279. A particle of mass m rotates with a constant speed in XY plane about the Z−axis in a circular path of radius r. Then for

the components of angular momentum (L) of this particle

(a) Lx = 0, Ly = 0, Lz ≠ 0 (b) Lx = 0, Ly = 0, Lz = 0

(c) Lx ≠ 0, Ly = 0, Lz = 0 (d) Lx = Ly = Lz = 0

Q280. The radius of gyration of a rod of length � about an axis passing through its centre of gravity and perpendicular to its

length is given by


(a) � (b) � /2 (c) � /3 (d) � /2 √3

Answers

221. (c): def. center of mass

222. (c): def.

223. (b): def.

224. (c): def.

225. (a) def.

226. (d)

227. (b): def rad of gyration MK2 = ∑ 2

ii rm

228. (a): T = K/I2π I = momentum of inertia

229. (c)

230. (c)

231. (a): KE of rotation = 1/2 Iω2 ; v = rω

232. (a): def.

233. (a) def.

234. (c): def./calculation of Moment of Inertia

235. (a): as above

236. (a): as above def.

237. (b): Torque will be max. at that position

238. (b): Conservation of energy; KE = 2

1 Iω2

v = n0

239. (a): def.

240. (c): def. of moment of inertia, frictional constant

241. (c)

242. (d) def.

243. (a): def. of MI and equilibrium of force on a moving body

244. (d)

245. (d): calculate tension with given masses

246. (b): resultant force balances the frictional force

247. (d): Force × time = change of momentum, Torque × time = change of Ang. moment

248. (d): equilibrium of forces in the helicopter

249. (d): def. of moment of inertia

250. (d): def.

251. (d)

252. (a): accel. Due to motion on curve adds to g to give resultant accl.

253. (b): def. Ang. Mom. = rad vector × Force

254. (c): def. as above

255. (c): def.

256. (b): conservation of angular momentum of body and stool

257. (a): conservation KE − rotational and potential

258. (a): due to centripetal force water will move outward to increase moment of inertia

259. (d): definition of Torque = r × F

260. (b)

261. (a): outward force will cause increase in the tension

262. (b)

263. (a): r and F are along the same line so r × F = 0

264. (c): def. r and p are 1 each other

265. (d): def. area swept/ time taken


266. (d): v = r × ω ⇒ dt

dv

dt

dv

dt

dv ω×+ω×= = red acel + ? acel.

267. (c): def. of ang. Velocity − sign convention of direction.

268. (c): as above

269. (b): dt

Ld�

= torque def.

270. (c): if F = 0, torque will also be zero

271. (a): perpendicular axis ? of MI

272. (c): def. distribution of mass about rotation axis is different

273. (c)

274. (a): Tension is because of the centripetal force

275. (c): def. of linear velocity for circular motion

276. (c)

277. (c): Parallel axis ? of MI


279. (a): def. angular momentum

280. (a): def.


Q161. A long sprig when stretched by x cm has a potential energy V. on increasing the stretching to nx cm, the potential

energy stored in the spring will be

(a) v/n (b) nv (c) n2v (d) v/n

2

Q162. Two bodies of masses m and 4m are moving with equal kinetic energy. The ratio of their linear momentum is

(a) 1 : 4 (b) 4 : 1 (c) 1 : 2 (d) 1 : 1

Q163. Two bodies of masses m and 4m are moving with equal linear momentum. The ratio of their kinetic energies is

(a) 1 : 4 (b) 1 : 1 (c) 4 : 1 (d) 1 : 2

Q164. The relationship between the force F and

position x of a body is as shown in figure. The

work down in displacing the body from x = 1m to

x = 5m. will be

1 2 3 4 5 6O

-5

-10

5

10

F(N)

x (m)

(a) 20 J (b) 15 J (c) 25 J (d) 30 J

Q165. Several forces varying both in magnitude and direction are used to move a particle along a smooth curved horizontal

path. The work done in the particle by the resultant force equals the change in the

(a) total energy of the particle

(b) kinetic energy of the particle

(c) potential energy of the particle

(d) any of the above depending upon the nature of forces and path.

Q166. A body of mass m accelerates uniformly from rest to a speed u in a time T. The instantaneous power delivered to the

body as a function of time t is given by

(a) tT

mu

2

1 2

(b) tT

mu

2

12

2

(c) tT

mu2

2

(d) 2

2

2

tT

mu

Q167. The gain in potential energy of an object of mass M raised from the surface of the earth to a height equal to the radius

R of the earth is

(a) MgR/2 (b) MgR (c) 2MgR (d) MgR/4

Q168. Two mass M and 4M are suspended from the ends of two identical springs. Both the masses are stretched down from

their mean positions and let go simultaneously. If they are in same phase every four seconds, the springs constant is

(a) π N/m (b) π2N/m (c) 2πN/m (d) 2π2

N/m

Q169. Ten springs of spring constant 1 N/m, ½ N/m, ¼ N/m---- connected in

parallel as shown are equivalent to a single spring of spring constant.

(a) 45 N/m (b) 511/256 N/m

(c) 12.3 N/m (d) 1023/512 N/m

m

Q170. The force required to stretch a spring varies with distance stretched as

shown If the experiment is performed with a spring of half the length, the

line OA will

(a) shift towards F−axis (b) shift towards X−axis

(c) remain unchanged (d) becomes double the length

F(N)

2

0.04 x (m)

Q171. The period of oscillation of the spring system of spring constant 120 N. m is T. If an other spring of spring constant

240 N/m is connected in series with this spring the time period of the system will become.

(a) √3 T (b) 2/3 T (c) 3T (d) √3/2 T


Q172. Two bodies of masses M1 and M2 have same kinetic energy. The ratio of their linear momentum is

(a) 21 M/M (b) 12 M/M (c) M1/M2 (d) M2/M1

Q173. Two bodies of unequal masses moving with velocity V1 and V2 have same kinetic energy. The ratio of their linear

momentum is

(a) V1/V2 (b) V2/V1 (c) 21 V/V (d) 12 V/V

Q174. A man raises to 10 bricks to the top of a building by going up a vertical spiral stair case in ? whereas a boy raises to

bricks to the same spot by a straight ladder in 10 minutes. Then

(a) neither of their does any work (b) both of their does any work

(c) the boy does more work their the man (d) the boy does less work their the man

Q175. A weight w extends the spring of length L by a length � . If the spring is cut into halves, the same weight will produce

the extension equal to

(a) 2/� (b) � (c) 2 � (d) � /√2

Q176. A sphere of mass m1 in motion hits directly another sphere of mass m2 and sticks to it. The total kinetic energy after the

collision is 2/3 of their initial kinetic energy. The ratio of m1 : m2 is

(a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 2 : 3

Q177. Three particles are projected vertically upwards from a point on the surface of the earth with velocities

3

gR2, gR ,

3

gR4 respectively where R is the radius of the earth and g, the acceleration due to gravity on its

surface. If the maximum heights attained are respectively h1, h2, h3, then

(a) h1 : h2 = 2 : 3 (b) h2 : h3 = 3 : 4 (c) h1 : h3 = 1 : 2 (d) h2 = R

Q178. The potential energy of a particle of mass 5 kg moving in the XY plane is given by V = −7x + 24 y J (X, Y in metres).

Initially at t = 0, the particle is at the origin moving with a velocity 6 [(2.4) i + (0.7) j ] m/s which of the statements

below is false

(a) Velocity of the particle at t = 4 is 25 m/s

(b) Acceleration of the particle is 5 m/s2

(c) The direction of motion of the particle at t = 0 is perpendicular to the direction of its acceleration

(d) The path is particle is a circle

Q179. Two masses of 1 g and 4 g are moving with kinetic energies in the ratio 4 : 1. The ratio of their linear momenta is

(a) 1 : 1 (b) 1 : √2 (c) 4 : 1 (d) 16 : 1

Q180. Two identical cylinders of area of cross−section A level contain liquid of density ρ. The level of liquid in one is h1 and

in other in h2 (h2 > h1). When the two cylinder are connected, the work done by gravity to equilise the levels in the two

cylinders is proportion to

(a) 1/4 ρS (x2 − x1) (b) 1/4 ρS (x2 − x1)2 (c) 4 ρS (x2 − x1) (d) 4 ρS (x2 − x1)

2

Q181. A block of mass m slides down from rain of the hemispherical bowl of radius R along its inner surface. The velocity of

the block at bottom will be

(a) gR (b) gR2 (c) gRπ (d) gR2

Q182. The work done by the string of a simple pendulum during one complete oscillation is equal to

(a) Total energy of the pendulum (b) Kinetic energy of the pendulum

(c) Potential energy of the pendulum (d) zero

Q183. If the kinetic energy of a body becomes four time its initial value, its momentum will

(a) increase to four times (b) decrease by four times (c) increase to two times (d) decrease by two times

Q184. The kinetic energy of a body of mass M as it slide

down the incline shown below is 10 J. The mass of the

body is (g = 10 m/s2)

2m

30

(a) 1 kg (b) 2 kg (c) √2 kg (c) 2√2 kg


Q185. A body is released from the top of a tower. After one second its kinetic energy is K. After one more second its kinetic

energy will be

(a) k (b) 2k (c) 4k (d) 8k

Q186. A body is released from the top of a tower. After one second its potential energy decreases by P. After one more

second it will decrease by

(a) p (b) 2p (c) 4p (d) 8p

Q187. The bob of a simple pendulum is at its mid point, its energy is

(a) half kinetic and half potential (b) totally potential

(c) totally kinetic (d) zero

Q188. When the bob of a simple pendulum is at its extremes position, its energy is

(a) zero (b) half kinetic and half potential

(c) totally potential (d) totally kinetic

Q189. From a water fall, water is pouring down at the rate of 100 kg/sec. on the blades of a turbine. If the height of fall is 100

m, the power delivered to the turbine is approximately equal to

(a) 1 kw (b) 10 kw (c) 100 kw (d) 1000 kw

Q190. When a body of mass m revolves with a uniform speed v on a circular path of radius r, the work done by the body in

one complete rotation is

(a) 1/2 mv2 (b) 2πmv

2 (c)

−π

2

12 mv

2 (d) zero

Q191. A particle moves in a circle of radius R with a constant speed under the centripetal force F. The work done in

completing a full circle is

(a) zero (b) 2πRF (c) πR2F (d) πRF

Q192. The power of an engine required to lift 200 kg of iron are per second from a mine 6m deep is nearly

(a) 120 w (b) 1200 w (c) 12 kw (d) 20 kw

Q193. A shell at rest explodes into three fragments. Two of three move at right angle to each other. The third fragment will

move in a direction

(a) at right angles to both the above (b) along the resultant of the two

(c) opposite to the resultant of the two (d) determined at random

Q194. A stone is tied to a rope and attached to a wooden bar which rotates at a constant angular velocity. Suddenly the bar is

stopped and the stone gets encircled around the bar. The angular velocity of the stone

(a) increases (b) decreases

(c) remains constant (d) first increase and then decrease

Q195. A lead ball and a tennis ball of equal mass strike a wall with the same velocity. The former falls down and the latter

bounces back. Which of the following statements about their momenta is correct ?

(a) The lead ball has greater momentum than the tennis ball

(b) both the balls suffer same change in momentum

(c) the lead ball suffers greater change in momentum

(d) the tennis ball suffers greater change in momentum

Q196. A double−decker bus is unlikely to topple over while moving round a curve if

(a) all the passengers are on the upper deck (b) there are no passengers on the two decks

(c) passengers are equally divided on the two decks

(d) all the passengers are on the lower deck

Q197. A body at rest disintegrate into two pieces of equal mass. The two pieces will move in

(a) the same direction with equal speeds (b) the same direction with unequal speeds

(c) the opposite direction with equal speeds (d) the opposite direction with unequal speeds

Q198. The work done in joules in increasing the extension of an elastic spring of stiffness 200 N/m from 5 cm to 15 cm is

(a) 5 (b) 3 (c) 2 (d) 1

Q199. Two spheres of masses 3 kg and 2 kg collide directly. Their relative velocity before collision is 15 m/s and after

collision in 5 m/sec. The loss of kinetic energy in joule due to collision is

(a) 500 (b) 350 (c) 220 (d) 120

Q200. The period of simple pendulum in a stationery lift is T. When the lift has an upward acceleration of 159/49, the period

of oscillation of the pendulum will be


(a) 15 T/49 (b) 49 T/15 (c) 7T/8 (d) T

Q201. A shell of mass 2m fired with a speed v at an angle θ to the horizontal explodes at the highest point of its motion into

two fragments of mass m each. If one fragment where initial speed in zero vertically, the distance at which the other

fragment falls from the gun is given by

(a) g

2sinu

2

3 2 θ (b)

g

2sinu2 2 θ (c)

g

2sinu 2 θ (d)

g

2sinu3 2 θ

Q202. If the earth were to contract suddenly to 1/n th of its present size without any change in mass, the duration of the new

day will be nearly

(a) 24/h hours (b) 24/n2 hours (c) 24 n hours (d) 24 n

2 hours

Q203. Sand is dropping from a stationery hopper on to a conveyer belt at a rate given by dM/dt, the force required to keep the

belt moving at a constant speed v is

(a) dt

dMv 2 (b)

dt

dM

v

1 (c)

dt

dM

v

12

(d) dt

dMv

Q204. A bird in a wire cage hangs from a spring balance. The reading of the balance is taken when the bird is flying about in

the cage and a second when the bird is at rest in the cage. The first reading will be

(a) much greater than the second (b) slightly greater than the second

(c) less than the second (d) the same as the second

Q205. A thick moves on a smooth horizontal surface with a uniform speed u carrying stone dust. If a mass ∆m of the

stone−dust leaks from the truck in a time ∆t, the force needed to keep the truck moving at its uniform speed is

(a) u ∆m/∆t (b) ∆m (du/dt) (c) dt

dum

t

mu ∆+

∆∆

(d) zero

Q206. Three particles each of mass m are located at the vertices of an equilateral triangle ABC. They start moving with equal

speeds v each along the medium of the triangle and collide at its centered G. If after the collision, A comes to rest and B

retraces is path along GB, then C,

(a) also comes to rest (b) moves with a speed v along CG

(c) moves with a speed v along BG (d) moves with a speed v along AG

Q207. A body of mass M moving with a speed u has a ‘heat−on’ collision with a body of mass m originally at rest. If M >>

m, the speed of the body of mass in after the collision will be nearly

(a) u (m/M) (b) u (M/m) (c) u/2 (d) 2u

Q208. Two particles 1 & 2 of equal mass moving with velocity v1 and v2 respectively make an elastic head on collision. After

the collisions, the particles 1 & 2 have their velocities equal to

(a) v1 and v2 (b) zero each

(c) v2 and v1 (d) any combination consistent with conservation of energy

Q208. In the above problem if the particle (2) is at rest initially, the velocity of particles 1 & 2 after the collision will be

(a) v1 and 0 (b) zero each (c) v1 each (d) 0 and v1

Q209. A particle of small mass moving with velocity v collide with a very heavy body at rest, the velocities of the particle and

the body after the collision will be

(a) 0 and v (b) v and 0 (c) −v and zero (d) zero and −v

Q210. A particle A suffers an oblique collision with a particle B, that is at rest initially. If their masses are same, then after the

collision.

(a) they will move in opposite direction

(b) A will continue to more in the original direction while B remains at rest

(c) they will move in mutually perpendicular direction

(d) A comes to rest and B starts moving in the direction of the original motion of A

Q211. During the oscillations of a simple pendulum the kinetic energy of the simple pendulum also varies periodically with

frequency wk. Its relationship with the frequency of the pendulum is

(a) wk = w/2 (b) wk = w (c) wk = 2w (d) no relationship

Q212. The potential energy of a simple pendulum varies with frequency wp during the motion of a simple pendulum. Wp is

related to the frequency w of the pendulum as

(a) wp = w/2 (b) wp = w (c) wp = 2w (d) no relation

Q213. The kinetic energy and potential energies of a simple pendulum vary periodically during the motion the pendulum. The

total energy of the pendulum


(a) also varies with the same periodicity as that of the kinetic energy

(b) also varies with the same periodicity as that of the potential energy

(c) also varies with same periodicity as that of the pendulum

(d) remains constant

Q214. A body of mass M is dropped from a height h above the earths surface which of the following statements is not true for

this body

(a) The kinetic energy of the body increases and is equal to Mgh just before it strikes the ground

(b) The velocity of the body just before it strike the ground is gh2

(c) the potential energy of the body remain constant during the fall

(d) the gain in kinetic energy is equal to the work done by gravitational force on the body during its false

Q215. Springs A and B are identical except that A is stiffer than B. If they are stretched by the same amount

(a) work expended on A is more than that on B

(b) work expended on A is same as that on B

(c) work expended on A is less than that on B

(d) the work done on each will depend upon the duration of the application of force

Q216. Springs A and B are identical except that A is stiffer than B. If they are stretched by the same force

(a) work expended on A is more that ht on B

(b) work expended on A is less than that on B

(c) work expended on A is equal to that on B

(d) work expended on each will depend upon the duration of the application of force

Q217. A hollow metallic sphere filled with water is used as bob of a simple pendulum. If the sphere has a small hole in the

bottom through which the water is leaking continuously, the time period of the pendulum will

(a) gradually go on increasing

(b) gradually go on decreasing

(c) remain unchanged

(d) gradually go on increasing initially and will increase later when the sphere is empty

Q218. A cricket ball is hit at an angle of 45° to the ? with a kinetic energy W. At the highest point kinetic energy is

(a) E (b) E/2 (c) E/√2 (d) zero

Q219. The bob A of a pendulum released from 30° to the vertical hits another

bob B of the same mass at rest on a table as shown. After the collision

bob A will

(a) turn back and rise to its initial height

(b) turn back and rise to height les than its initial height

(c) rises to the same height on the other side

(d) come to rest and transfer all the moment to other ?

30°

m

Am

Q220. Pair production in the process in which a quantum of electromagnetic radiation in field of a nucleus produces a pair of

electron and position. For the process which of the statements below is false

(a) It exhibits equivalence of mass−energy

(b) It exhibits violation of conservation of mass as two massive particles are creates

(c) It exhibits law of conservation of momentum as the massive particles share the momentum of the radiation

(d) The process can take place only for certain minimum energy of the radiation

Answers

161. (c): def.

162. (c): kE = p2/2m

163. (b)

164. (c): w = Fx cosθ

165. (b): def.

166. (c): Power = Energy/time

167. (a): The attractive force = −GMm/r2 work done by the force to more the body from R to 2R position

168. (b): def. F = kx

169. (b): definition − addition of spring force in parallel


170. (a)

171. (b): def−addition of springs in series

172. (a): kE = p2/2m

173. (b)

174. (b): work done against gravity is equal

175. (a)

176. (c): conservation of energy−momentum

177. (d): kE will be zero at max. height

178. (d): nothing can said about the path from the data

179. (a): as above relation between kE & P

180. (b): work done = Gravitation force × height

181. (d): KE = PE at the position

182. (d): conservation force

183. (c)

184. (a): KE = PE at the bottom

185. (c): def.

186. (c): def.

187. (c): at the mean position PE = 0

188. (c): at the extreme position KE = 0

189. (c): Power = Energy/time

190. (d): def.

191. (a): centripetal force is normal to displacement

192. (c): def.

193. (c): conservation of linear momentum

194. (b): conservation of energy−momentum

195. (d)

196. (d): centre of gravity is lowest


198. (c): def.

199. (d)

200. (c)

201. (a): conservation of linear momentum and energy

202. (b)

203. (d): Linear momentum conservation

204. (c): Gravity does not act on the balance when the bird is flying

205. (d): conservation of linear momentum


207. (d): collision problem = conservation of linear momentum/energy

208. (c): as above

208. (d): as above

209. (c): as above

210. (c): collision problem

211. (c): in one cycle KE goes to zero twice

212. (c): in one cycle PE give to zero twice

213. (d): PE + KE remain constant

214. (c)

215. (a): w = 2

1 kx

2

216. (b): F = kx, w = 2

1 kx

2 =

2

1 k . F

2/k

2

217. (d): centre of gravity shift down ? and then upward after the water has completely

218. (d): def.

219. (d): collision problem − conservation of energy − linear momentum.


220. (b): conservation of energy into mass E = mc2.

Page 1 of 1

Q281. Astronauts in stable orbits round the earth are in a state of weightlessness because

(a) there is no gravitational force acting on them

(b) the gravitational force of sun and earth balance

(c) satellite has a acceleration equal to that of gravitational acceleration there

(d) there is no atmosphere at the height at which the satellite more

Q282. Which of the statements is false. The gravitational force between two bodies

(a) depends on the magnitude of the masses of the bodies

(b) the distribution of the mass in each body

(c) becomes one fourth when the distance between them is doubled

(d) depends on the nature of the medium between the bodies

Q283. The gravitational field at P due to a uniform solid sphere of radius R and centre O is

(a) inversely proportional to OP if OP ≥ R (b) inversely proportional to OP if OP < R

(c) inversely proportional to square of OP if OP > P (d) directly proportional to square of OP if OP < R

Q284. A string passes through a smooth hole O on a smooth horizontal table. A particle attached to one end of the string

describes circular motion of radius r0 on the with O as centre. The other end of the string is pulled vertically down

slowly at constant speed when the distance of the particle from O is r ( < r0)

(a) its kinetic energy is unchanged (b) its kinetic energy has decreased

(c) its kinetic energy has increased (d) its potential energy has increased

Q285. The dimensions of G, the universal gravitation constant are

(a) M3 L

3 T

−2 (b) M

−1 L

2 T

−3 (c) M

−1 L

3 T

−2 (d) M

−1 L

3 T

−1

Q286. The escape velocity from a planet of mass M and radius R is given by

(a) R/GM2 (b) R/GM2

1 (c) G/MR2 (d) GM/R

Q287. The value of acceleration due to gravity at a point above the surface of the earth is 9.8 m/s2. If the earth suddenly

shrinks to half its size uniformly without any change in its mass, the value of g at that point will now be

(a) 4.9 ms−2

(b) √2 × 9.8 ms−2

(c) 9.8 ms−2

(d) 9.8/√2 ms−2

Q288. The value of acceleration due to gravity is minimum

(a) at the equator (b) at the pole

(c) at the centre of the earth (d) at the highest point on the surface of the earth

Q289. The escape velocity from earth

(a) velocity with which any body is thrown from the surface of the earth

(b) velocity with which earth rotates abut its axis

(c) velocity with which earth moves around the sun

(d) the minimum velocity imparted to a body so that its escapes the gravitational attraction of the earth

Q290. For a body launched from the surface of the earth with velocity equal to the escape velocity, on just escaping the

gravitation pull of the earth

(a) only its kinetic energy will be zero (b) only its potential energy will be zero

(c) its total energy will be zero (d) both kinetic and potential energies will be zero

Q291. The escape velocity for a rocket on earth is 11.2 km/sec. Its value on a planet where acceleration due to gravity is

double that on the earth and whose diameter is double that of earth, will be (in km s−1

)

(a) 11.2 (b) 5.6 (c) 22.4 (d) 44.8

Q292. If the change in the value of g at height h above the surface of the earth is the same as at a depth x below it (both h and

x being much smaller than earth’s radius) than,

(a) h2

1x = (b) x = h (c) h

2

2x = (d) x = 2h

Q293. The diameter of the earth is 10 time that of moon and the gravitational acceleration at the surface of the earth is six

times that at the surface of the moon. The ratio of the escape velocity from earth to that from the moon is nearly

(a) 1 (b) 1.6 (c) 6 (d) 8

Q294. The distances of Saline and Nepline from the sun are 109 km and 10

10 km respectively. Assuming their motion in

circular orbits, their periods are in the ratio

(a) 10 (b) 10√10 (c) 100 (d) 10000

Q295. A satellite of mass m revolves in circular orbit at a height h from the earth’s surface. If R is the radius of earth and g,

the acceleration due to gravity on its surface, the velocity of the satellite in orbit is given by

Page 2 of 2

(a) gR2/R + h (b) gR (c) hR/gR + (d) hR/gR 2 +

Q296. A hollow spherical metallic vessel is filled with sand. The sand leaks through a small hole at the bottom. As the sand

leaks, the centre of gravity of the system will

(a) remain fixed

(b) shift upward continuously

(c) shift downward continuously

(d) shift downward in the beginning and then upward when it is nearly empty.

Q297. Mass has about 1/10 th

as much mass as the earth and half as great a diameter. The acceleration of a falling body on

mass is about

(a) 9.8 ms−2

(b) 1.96 ms−2

(c) 3.92 ms−2

(d) 4.9 ms−2

Q298. For the earth (mass M and radius R), the ratio of the gravitational acceleration to the gravitation constant is

(a) R2/M (b) MR

2 (c) M/R

2 (d) M/R

Q299. An object weighs W N on the earth. It is suspended from the spring balance which is fixed to ceiling of a space capsule

in stable orbit around the earth. The reading in the spring balance will be

(a) W (b) more than W (c) less than W (d) zero

Q300. A hole is drilled through the centre of the earth along a diameter and a stone is dropped into it. When the stone is at the

centre of the earth, it has a finite

(a) mass (b) weight (c) acceleration (d) potential energy

Q301. If g is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m

raised from earths surface to a height equal to its radius is

(a) mgR/2 (b) 2 mgR (c) mgR/√2 (d) √2 mgR

Q302. The escape velocity for a body projected vertically upwards from the surface of the earth is 11.2 km s−1

. If the body is

projected in a direction making an angle 45° with the vertical, it escape velocity will be

(a) 11.2 √2 km s−1 (b) 11.2 × √2 km s−1

(c) 11.2 km s-1

(d) 2 × 11.2 km s−1

Q303. An oscillating pendulum is allowed to fall freely under gravity along with its support. The times period of oscillation will

(a) increase (b) decrease (c) reduce to zero (d) become infinite

Q304. When a body is taken from the earth to the moon

(a) its weight and mass remain unchanged

(b) its weight decrease but its mass remains unchanged

(c) its weight remains unchanged but its mass decreases

(d) both its weight and mass decreases

Q305. A stone is dropped in to a hole which passes through the centre of the earth along its diameter. Then

(a) the stone will go on moving with ever increasing velocity

(b) on reaching the centre of the earth its velocity will become zero

(c) it will start oscillating with simple harmonic motion

(d) it will escape from other side of the hole

Q306. If the length of a simple pendulum is doubled, its time period will change in the ratio of

(a) 1/√2 : 1 (b) 1/2 : 1 (c) √2 : 1 (d) 2 : 1

Q307. From the circular lamina of radius 14 cm a circular disc of radius 7 cm is

cut off an shown. The position of centre of gravity of the remaining body is

on the line AB will be at a point

(a) 3.5 cm away from the point A on the right

(b) 3.5 cm away from the point A on the left

(c) 2.33 cm away from the point A on the left

(d) coincident with point A

A

B

7 cm

14 cm

Q308. The centre of gravity of a triangular uniform lamina is at the intersection of

(a) its altitudes

(b) its medians

(c) its bisection of angles

(d) none of the above, can be any where depending upon the weight

Q309. Kepler’s second law is aerial velocity of a planet around the sum is a consequence of

(a) law of conservation of angular momentum

(b) law of conservation of linear momentum

Page 3 of 3

(c) law of conservation of energy

(d) Newton’s gravitational law

Q310. A particle starts from rest from the point P on the frictionless sphere of

radius R shown in figure and slides under the force of gravity. It will fly off

the sphere after

(a) its potential energy has decreased by mgR/3

(b) it has traveled a distance R/3 along the surface of the sphere

(c) it has fallen through a verticals distance 2 R/3

(d) it has reached the point A on the sphere

P

A

Q311. An object is taken from a point A to another point B in a gravitational field. Then which of the following is wrong.

(a) If both A and B lie on the earths surface (assumed spherical), the work done is zero.

(b) If A is on the earth’s surface and B above it, the work done will be minimum of the object is taken along straight line path

(c) The work done depends on the locations of A & B

(d) The work done is independent of the path followed between A & B

Q312. An earth satellite can move only in the plane

(a) of equator (b) perpendicular to equator plane

(c) parallel to the equator plane (d) containing the centre of the earth

Q313. For the earth moving around the sun in its orbit, which of the statement is false

(a) There is attractive force acting on the earth along the radius vector. But in opposite direction

(b) The torque on the earth causes it to move in an elliptical orbit

(c) The earth moves faster when it is closer to run then when it is farthest to the sun

(d) The earth moves in a plane around the sun

Q314. Which of the following statements concerning gravitation constant G and acceleration due to gravity g is false.

(a) G is universal constant, while g varies from place to place m earth between different pairs of bodies

(b) G varies between different pairs of bodies

(c) G has the same value on all planets

(d) g varies from planet to planet

Q315. A particle slides from rest under gravity from the highest point of a vertical circle of radius r along a straight chord of

the circle. Which of the following statement will be true ?

(a) the time of descent will be maximum along the vertical diameter of the circle

(b) the time of descent will be minimum along the vertical diameter of the circle

(c) the time of descent will be more for the chord of longer length

(d) the time of descent will be same along all chords

Q316. A planet has a satellite whose period of revolution is T and its distance from the centre of planet is r. The mass of the

planet can be expressed as [G = Gravitational count]

(a) 2

3

T

rM = (b)

2

3

GT

r2M

π= (c)

3

2

r

GT2M

π= (d)

2

32

GT

r4M

π=

Q317. An artificial earth satellite A makes one revolution around the earth in two hours. A second satellite B is observed to take

8 hours to complete one revolution. The ratio of the distances rA and rB of the two satellites from the centre of earth is

(a) √2 (b) 1/√2 (c) 1/23√2 (d) 1/(√2) 3

Q318. An object is released from a height R/2 above the surface of a planet of radius R. If gravitation field at the surface of

the planet is g, the speed with which the object would strike the planet is given by

(a) gR3 (b) gR (c) 3/gR4 (d) 3/gR2

Q319. In a satellite moving around any planet, the gravitational force is effectively balanced. If an ice cube exists there after it

melts with passage of time, its shape will

(a) remain unchanged

(b) change to spherical

(c) become oral shaped with long axis along the orbit plane

(d) become oral−shaped oval

Q320. The weight of a body at the centre of the earth is

(a) zero

(b) infinity

(c) more than its weight at the surface of the earth

Page 4 of 4

(d) less than its weight at the surface of the earth

Q321. A satellite in orbit

(a) does not require energy for its motion

(b) derives energy from run

(c) moves under the gravitational force of earth only

(d) is kept in orbit by ground control

Q322. Newton’s law of Gravitational states that gravitational force between two mass points m1 and m2 a distance r away is

2

21

r

mmF = . Which of the following statements is not true for this force

(a) Gravitational forces between m1 &m2 is an action−reaction pair

(b) The force F acts along the line joining m1 & m2

(c) G has same value for all pairs of masses m1 and m2 on earth

(d) G has different values for pairs of masses m1 and m2 on the planets.

Q323. A charged particle of mass m experiences an acceleration in an electric field which is inversely proportion to the mass.

The relevant mass in question is

(a) gravitational mass

(b) inertial mass

(c) any of the two−gravitational mss or inertial mass

(d) neither gravitation nor inertial mass

Q324. A body of mass m when hung from a spring balance on the surface of the earth produces air extension in the spring of

the balance which is proportional to the mass of the body. The mass in question is

(a) inertial mass

(b) gravitational mass

(c) neither the inertial nor gravitational mass

(d) either inertial or gravitational mass

Q325. If the distance r between two mass is changed by an amount dr, the fractional change in the gravitational force (dF/F)

between them is given by

(a) − dr/2r (b) dr/2r (c) − 2dr/r (d) 2dr/r

Q326. In going up from earths surface at a distance by an amount dr, the fractional change in the value of acceleration due to

gravity dg/g is given by

(a) r

dr

2

1− (b)

r

dr

2

1 (c)

r

dr2 (d)

r

dr2−

Q327. It is known that value of acceleration due to gravity g varies on the surface of the earth being maximum at poles and

minimum at equator. If earth were a perfect sphere the value of g will be

(a) more at pole than at equator

(b) more at equator than at the poles

(c) equal at all points in the surface of the earth

(d) will be zero at equator and gradually increase with distance towards the pole

Q328. The motion of earth around its axis results in

(a) decrease in the value of g at the equator

(b) increase in the value of g at the equator

(c) decrease in the value of g at the pole

(d) increase in the value of g at the poles

Q329. For a body hanging with a spring balance at the equator of the earth. Which of the following statements is false

(a) The upward pull of the spring balances not exactly the gravitational force between body and earth

(b) The body is not in equilibrium because it experience a centripetal acceleration

(c) There is a net force acting on the body towards the centre of the earth

(d) there is a not force acting on the body outwards from the centre of the earth

Q330. If earth were to start rotating faster around its axis, then

(a) weight of bodies on equator will increase

(b) weight of bodies on poles will increase

(c) weight of bodies on equator will decrease

(d) weight of bodies on poles will decrease

Page 5 of 5

Q331. A planet revolves around the sun in an elliptical orbit of eccentricity e. The ratio of time spent by the planet between

ends of the inner axis close to the sun to the period of revolution is

(a) 1 (b) 1/2 (c) less than 1/2 (d) more than 1/2

Q332. The longest period of a simple pendulum in the vicinity of earth’s surface is nearly

(a) 1 sec (b) 1 minute (c) 84.3 min. (d) 60 min.

Q333. The binding energy of the earth system (assured circular orbit) can be given by [Me(Ms) ≡ eart (sun) ; res = distance

between then)

(a) res

MMG se− (b)

res2

MMG se− (c)

res

MGM2 se− (d)

re

MG

2e−

Q334. The ratio of the kinetic energy of earth due to its motion around the sun (assumed circular path) to the potential energy

of earth−sun system is

(a) 1/2 (b) 1 (c) 2 (d) 1/√2

Q335. Consider the motion of a satellite of mass m about a planet of mass M in a circular orbit of radius r. The total energy of

the planet can be written as

(a) zero (b) r2

Gmm (c)

r2

GMm− (d) infinite

Q336. Which of the following statements abut gravitational force between two bodies is wrong

(a) Gravitational force is a central force

(b) Gravitational fore is a conservation force

(c) Gravitational force is always a attractive force

(d) Gravitational force can not be deceived from a potential

Q337. The keplers first law that the orbit of a planet around sun is an ellipse is a consequence of

(a) inverse square nature of gravitational force

(b) conservation of angular momentum

(c) conservation of energy

(d) conservation of linear momentum

Q338. The gravitational potential energy of a body of mass m on the surface of earth (mass M radius R) can be gravity

(a) R

GMm (b)

R

GMm− (c)

2r

GMm (d)

2r

GMm−

Q339. The fact that the value of acceleration due to gravity steadily increase from equator to poles can be explained by

(a) spherical shape of the earth

(b) rotation of the earth about its axis

(c) variation of value of gravitational constant on the surface of the earth

(d) earth being a sphere of non−uniform density

Q340. For the four fundamental interactions namely gravitational interaction, weak interaction, electromagnetic interaction

and nuclear (strong) interaction which of the following statements is not true.

(a) Gravitational interaction acts between all particles including photons

(b) Electromagnetic interaction acts between all particles currying electric charge

(c) Gravitational interaction does not depend upon the charge of the particles

(d) Electromagnetic interaction does not depend upon the mass of the particles.

Answers

281. (c)

282. (d): def.

283. (c): def.

284. (c): because of the work done by gravitational force

285. (c): F = GMM′/R2

286. (a): by definition

287. (c): g is determined by mass of earth for the outside its surface

288. (c): no gravitational force at the centre ⇒ g = 0


290. (d): KE = 0 by def., PE = 0 by def.

Page 6 of 6

291. (c)

292. (a): inside the surface G varies linearly with x


294. (b): Kepler’s third law

295. (d): centripetal force balanced by gravitational pull. of cals.

296. (d): CG shifts downwards first but moves centre after the sand in out completely


298. (c): def.

299. (d): case of free fall no tension recorded by spring ?

300. (a): accel, weight (g), potential energy = zero at centre

301. (a): work done by gravitational force = gain in pot. Energy

302. (c): escape velocity is same in all direction

303. (d): g � 0 for free fall; T � 0

304. (b): f has different value on moon

305. (c)

306. (a): expression for time period

307. (c)

308. (b)

309. (a): Areal velocity is related by Ang. Momentum by a const.

310. (a): where centripetal acel is balance by gravitation pull down ?.

311. (b): Work done is independent of path is gravitational filed

312. (d): satellite is always attracted by gravitational force to centre of earth

313. (b): torque is zero as r & F are along the same two


315. (d): component of accel. will be different along each chord giving different velocities.

316. (d)

317. (c)

318. (d): the KE = charge in Potential Energy

319. (b): effect of gravity will not be there but surface tension will make the surface area to be minium v spherical

320. (a): at the centre g = 0

321. (c)

322. (d)

323. (b): definition of inertial mass

324. (b): definition of gravitational mass

325. (c): r/dr2g

dg

F

dF−==

2r

GMmF =

326. (d): as above

327. (a): due to effect of earth circular motion

328. (a): as above

329. (d): centripetal force acts on the body

330. (c): effect of centripetal force will increase

331. (c): when the planet is closes to sun at moves faster.

332. (c): time period for pendulum of infinite length

333. (b)

334. (a): calculate the ratio straight forwardly

335. (c): total energy = KE + PE = −ve because of bond system

336. (d): Gravitational force is conservative F = x/v ∂−∂

337. (a)

338. (b): Potential ⇒ Fx

v=

∂

∂−

339. (b): centripetal force is max. at the equator ? at the pole

340. (a): Gravitational force acts between all bodies having non zero rest mass

Page 1


Q1. The periodic beatings of the heart of a healthy person may be compared to a

(a) forced harmonic oscillator (b) damped harmonic oscillator

(c) forced harmonic oscillator with damping (d) pure free simple harmonic oscillator

Q2. Which one of the following functions of time represents a simple harmonic motion ?

(a) sin2 ωt + cos

2 ωt (b) e

−ωt + sin

2 ωt (c) sin ωt + cos 3 ωt (d) sin ωt + cos ωt

the symbols have usual meaning

Q3. The length of a seconds pendulum at a place where acceleration due to gravity is 10 m/s2 is about

(a) 1 m (b) 0.1 m (c) 10 m (d) 0.25 m

Q4. A particle executes S.H.M. of amplitudes 10 cm, the distance of a point from its mean position at which its kinetic

energy is exactly equal to its potential energy is about

(a) 0.71 cm (b) 7.1 cm (c) 71 cm (d) 0.51 cm

Q5. A simple pendulum mounted I a lift which acceleration downwards at 5 m/s2 at a place where g is 10 m/s

2, the

percentage change in the period is about

(a) 41% increase (b) 41% decrease (c) 20% decrease (d) 80% increase

Q6. The expression for the frequency of a damped harmonic oscillator with mass ‘m’ resting force constant ‘k’ and damping

factor ‘b’ is given by

(a) ( )2m2/bm/k − (b) ( )2

m2/bm/k2 −π (c)

2

m2

b

m

k

2

1

−

π (d)

2

m2

b

m

k

+

Q7. The most generated form of equation of motion of a forced simple harmonic oscillator with damping included is (where

the symbols have usual meaning)

(a) 0kxdt

xdm

2

2

=+ (b) tcosFkxdt

xdm 02

2

ω=+

(c) 0kxdt

dxb

dt

xdm

2

2

=++ (d) tcosFkxdt

dxb

dt

xdm 02

2

ω=++

Q8. In a simple harmonic motion which one of the following statements is incorrect ?

(a) the velocity leads the displacement by a phase of π/2

(b) the acceleration leads the velocity by a phase of π/2

(c) the displacement lags the acceleration by a phase of π/2

(d) the acceleration leads the displacement by a phase of π

Q9. The most general solution of 0kxdt

xdm

2

2

=+ representing a pure simple harmonic motion is of the form (where the

symbols have the usual meanings)

(a) A sin

t

m

k (b) A cos t

m

k

(c)

+ t

m

kcost

m

ksinA (d) A sin

φ+t

m

k

Q10. The speed (v) of a simple harmonic oscillator with amplitude A, in terms of its displacement (x) at any instant of time is

given by

(a) T

xAv

22 −= (b)

22xA

T

2v −

π= (c)

22xA

Tv −

π= (d)

22Ax

T

2v −

π=

Q11. The ratio of kinetic energy to the potential energy of a simple harmonic oscillator at a point mid way between the mean

equilibrium position and one of its extremities is

(a) 3 (b) 1/3 (c) 1 (d) 2

Q12. In simple harmonic motion which one of the following statements is true ?

(a) The magnitude of acceleration of a particle is the least at the extremities of the oscillator

(b) The total energy equals the potential energy at the end points together with the kinetic energy at the mean position

(c) the restoring force is maximum when the particle is instantaneously at rest during oscillations

(d) The time period primarily depends on the amplitude but independent of the phase

Page 2


Q13. A spring balance has a scale that reads from O to 50 kg uniformly graduated on a scale of length 20 cm. The weight a

body suspended from this spring oscillating with a period of 0.63 s is about

(a) 25 Kg (b) 250 N (c) 2500 N (d) 250 Kg

Q14. An impulsive force gives an initial velocity of − 1.0 m/s to the mass attached to the free and of a spring which

subsequently oscillates with a time period of 0.63 s, the amplitude of acceleration is about

(a) 1 m/s2 (b) 10

−2 m/s

2 (c) 10

−1 m/s

2 (d) 10 m/s

2

Q15. In a S.H.M. the displacement (x) of mass ‘m’ as a function of time (t) is given by x = cos ,t6

−

π then its

(a) amplitude is 1 m and initial phase is − 30°

(b) amplitude is 1m and its time period is 1 s

(c) velocity amplitude is 1 m/s and initial phase is π/6 reds

(d) velocity amplitude is −1 m/s, and initial phase is −π/6 rad

Q16. The equalization due to gravity on the surface of moon is

(a) 1/6 of the acceleration due to gravity an earth

(b) 1/4 of the acceleration due to gravity an earth

(c) 1/3 of the acceleration due to gravity on earth

(d) 1/2 of the acceleration due to gravity

Q17. The percentage change in the time period of oscillation of a simple pendulum when it is taken from the surface of the

earth to the surface of moon, is about

(a) 145% (b) 14.5% (c) 145% increase (d) 145% decrease

Q18. The time period of oscillation of a seconds pendulum on the surface of moon is about

(a) 1.0 s (b) 2.0 s (c) 4.9 s (d) 2.5 s

Q19. If k1 and k2 are the spring constants of two springs arranged in parallel , their equivalent spring constant k (for k2 > k1)

is given by

(a) 21 k

1

k

1+ (b)

21 k

1

k

1− (c) k2 − k1 (d) k1 + k1

Q20. If k1 and k2 are force constants of two springs arranged in series their equivalent force constant (k) is given by

(for k2 > k2)

(a) k1 + k2 (b) 21 k

1

k

1+ (c)

21

21

kk

kk

+ (d)

21 k

1

k

1−

Q21. For a particle in linear S.H.M. the average kinetic energy over a period of oscillation is equal to

(a) total energy of the oscillator (b) half the total energy of the oscillator

(c) total kinetic energy of the oscillator (d) total potential energy of the oscillator

Q22. A spring of force constant k is cut into 3 equal parts. The force constant of each part is equal to

(a) k/3 (b) k (c) 3k (d) (2/3) k

Q23. Te time period of oscillation of a simple pendulum of length ''� is T, a plot of log T versus log ''� gives a straight line

with slope

(a) 2 (b) √2 (c) 1/√2 (d) ½

Q24. A simple pendulum has a hollow spherical bob filled with mercury. As the pendulum oscillates mercury gradually flows

out f the bob through a tiny hole at the bottom, the frequency of oscillation of the pendulum

(a) first decrease, then increases and finally attains its original value

(b) first increase, then decrease and finally attains its original value

(c) remain unaffected

(d) decreases continuously to a minimum

Q25. A pendulum is oscillating about an horizontal axis in a vertical plane in a lift. The acceleration with which the lift must

be raised to reduce the time period of oscillation to one half of its original value is oscillation to one half of its original

value is

(a) g/4 (b) 5g (c) 3g (d) 4g

Q26. A mass ‘m’ suspended from a light spring has a period T for its vertical simple harmonic oscillation. One adding a mass

‘M’ to ‘m’ the period becomes 3T, the mass added must be equal to

(a) 2m (b) 8m (c) 3m (d) 6m

Page 3


Q27. The shape of the curve obtained from the plot of kinetic energy versus position of the bob of a simple pendulum from

its mean equilibrium position is a parabola opening

(a) upwards with its vertex at the origin

(b) upwards with its vertex anywhere on the x−axis

(c) downward with its vertex on the energy axis

(d) downwards with its vertex at the origin

Q28. In a S.H.M. the force (F) and the potential energy (U) are related to each other by

(a) ( ) ( );

dx

xdVxF = (b) ( ) ( )

dx

xdUxF −= (c) ( ) ( )

;dx

xudxF

2

2

−= (d) ( ) ( )∫−= xdvxF

Q29. The bob of a simple pendulum was allowed to oscillates simple harmonically by pulling the bob to the extreme right

and releasing it The period function exactly representing this S.H.M. is

(a) x = A sin ωt (b) x = A sin (ωt + φ) (c) x = A cos (ωt + φ) (d) x = A cos ωt

Q30. Combinations of two simple harmonic motions along two mutually perpendicular directions generates a special type of

figures called

(a) Fourier figures (b) Lissagou’s figures (c) Harmonic figures (d) circular figures

Q31. The frequency of oscillation of a critically damped ideal S.H.O. is

(a) very large (b) very small

(c) zero (d) equal to the frequency of undamped oscillator

Q32. A light spring has a force constant k1 and an object of mass m is suspended from it. The sprig is cut in half and the same

object is suspended from one of the halves. The ratio of frequencies of oscillations before and after the spring is cut is

equal to

(a) 2 (b) 1 (c) 1/√2 (d) √2

Q33. Any real spring has a mass of the mass of the spring (ms) of the simple harmonically oscillating spring−mass (m)

system is also taken into account, its period will

(a) increase (b) decrease

(c) remain unaffected (d) gets affected only if m >> ms

Q34. Damping devices are after used on machinery to

(a) increase the frequency of vibration (b) avoid resonance vibrations

(c) decrease the frequency of vibrations (d) critically damp the vibrations

Q35. In an electric shaver, the blade moves back and forth over distance of 2 mm. The motion is S.H.M. with a frequency

120 Hz. The velocity amplitude of the block is about

(a) 1.51 mm/s (b) 15.1 m/s (c) 1.51 m/s (d) 0.75 m/s

Q36. The piston in the cylinder heat of a locomotion has a stroke of 76.5 cm. The maximum speed of the piston when the

drive wheels make 193 rpm and the piston moves with S.H.M. will be

(a) 7.73 m/s (b) 15.46 m/s (c) 0.77 m/s (d) 20.20 m/s

Q37. A block is an a piston that is moving vertically with S.H.M. of period 1.18 s. The critical value of the amplitude of

motion at which the block just separate from the piston is (use g = 10 m/s2)

(a) 2.78 m (b) 278.0 m (c) 3.52 m (d) 35.2 cm

Q38. A loud speaker produces musical sound by the oscillation of a diaphragm. If the amplitude of oscillation is limited to ‘a’

metres the frequencies that would result in the acceleration of the diaphragm exceeding ‘g’, is

(a) greater than a/g2π (b) greater than ( ) a/g2/1 π

(c) less than a/g2π (d) less than a/g2

1

π

Q39. A body hung from a vertical light spiral spring stretches it by 1.8 cm. The frequency of oscillation body−spring system

is

(a) 3π/35 (b) 35π/3 (c) 35/3π (d) π/105

Q40. At a certain harbor, the tides cause the ocean surface to rise and toll in S.H.M., with a period of 12.5 hr. The time taken

for a tide to toll from its peak height to one−half its peck height above its average level is about

(a) 2.08 hr (b) 4.2 hr (c) 3.1 hr (d) 2.5 hr

Q41. A hypothetically large sling shot is stretched by 1.12 m to launch a 110 gm projectile with a speed sufficient to escape

from the earth (11.2 km/s) Assuming that an average person can exert a fore of 220 N, the number of persons required

to stretch the sling shot is

Page 4


(a) 1.12 × 105 (b) 5.6 × 10

4 (c) 2.8 × 10

4 (d) 1.1 × 10

7

Q42. In a S.H.M. when the displacement is one half of the amplitude, the fraction of total energy which is kinetic and which

is potential are respectively equal to

(a) 0.25 and 0.75 (b) 0.50 and 0.50 (c) 0.75 and 0.25 (d) 0.67 and 0.33

Q43. In the forced S.H. oscillation of a damped block−spring system, if ω is the angular frequency then the ratio of amplitude

of oscillation to the maximum velocity is given by

(a) ω (b) 1/ω (c) 2π/ω (d) ω/2π

Q44. A particle executes S.H.M. with a frequency f. The frequency with which its kinetic energy oscillates is

(a) f (b) f/2 (c) 4f (d) 2f

Q45. When bullet in motion strikes a solid block of wood resting on a functionless table, and gets embedded into it,

(a) both the energy and momentum are conserved

(b) only momentum is conserved

(c) only energy is conserved

(d) neither momentum nor energy is conserved

Q46. A mass is hung from a vertical light spring and is set into oscillations. The frequency of oscillations can be decreased by

(a) taking the arrangement to a higher altitude

(b) increasing the amplitude of oscillation

(c) decreasing the mass hung

(d) adding identical spring to the first in series.

Page 5


Answers

1. (c)

2. (d)

3. (a): Hint: T for a second’s pendulum is 2s, and T = 2π g/� , Find �

4. (b): Hint: the equation to be used is 1/(2) kx2 = 1/(2) k (A

2 − x

2), get x = a/√2

5. (a): Hint: (T′/T) = 'g/g and g′ = g −5, Find 100T

T'T×

− = 41%

6. (c): Hint: from theory ( ) ( )2m2/bm/k −=ω

7. (d)

8. (c)

9. (d)

10. (b) Hint: In S.H.M. we have 22

xAv −ω= s

11. (a): Hint: P.E. = 1/(2) kx2 = 1/(2) k (A/2)

2 = (1/4) E ; Hence K.E. = E

4

3

4

EE =−

12. (c)

13. (b): Hint: Mg = kx i.e. 50 g = 0.2 k ; T = k/M2π Find 2

2

4

kTgMg

π=

14. (d): Hint: accn. amp. = velocity amp. × ω

15. (c): Hint: compare with x = A cos (ωt + φ)

16. (a)

17. (c): Hint: meem g/gT/T = Find (Tm − Te) × 100/Te = 145%

18. (b)

19. (d): Hint: for springs in parallel keg = k1 + k2 + k3 +…

20. (c): Hint: for springs in series ...k

1

k

1

k

1

k

1

321eq

+++=

21. (b)

22. (c): Hint: for springs in series 321eq k

1

k

1

k

1

k

1++= Here k1 = k2 = k3 = k

23. (d): Hint: T = 2π g/� so log T = 1/(2) log � + log (2π/g)

24. (a): Hint: �/g2

1v

π= � increases and then decreases to initial value due to shift in the centre of gravity of the

pendulum.

25. (c): Hint: T′/T = 'g/g and g′ = 4g gives the result.

26. (b) Hint: T = 2π k/m

27. (c): Hint: K.E. = k/(2) (A2 − x

2)

28. (b) Hint: F(x) =

− 2kx

2

1

dx

d = −kx which S.H.O force

29. (d): Hint: at t = 0, x = +A and φ = 0 are given conditions

30. (b)

31. (c): Hint:

2

m2

b

m

k'

−=ω for km2b = ω′ = o critically damped.

32. (c): Hint: m/'k'w;m/kw == where 21

21

kk

kkk

+=

Here k1 = k2 = k′ ∴ k′ = 2k

Page 6


33. (a): Hint: T = 2π ( ( ) k/3mm s+

34. (d)

35. (d): Hint: v0 = 2πvA; here A = 1 × 10−3

m & v = 120 Hz

36. (a): Hint: v = 2πvA; here A = 0.3825 m; v = 193/60 Hz

37. (a): Hint: |mg| = |kA| ; m/k = A/g Hence A = gT2/4π2

38. (b): Hint: a0 = Aω2 = g; hence A/g

2

1v

π=

39. (c): Hint: mg = kA; g/am/k ==ω

40. (a): Hint: x = a sin ωt hence 3

tT

2 π=

π and t = T/6 find x

41. (b): Hint: 1/(2) kA2 = 1/(2) mveq

2 find k to get kA/220 as the no of persons.

42. (c): Hint: P.E. = 1/(2) kx2 = 1/(4) ;

4

E

2

kA 2

=

and hence K.E. = 3E/(4)

43. (b): Hint: xm = Fm/bW ; vm = Fm/b and hence (xm/vm) = Yw

44. (d)

45. (b): Hint: mechanical energy is not conserved due to loss of energy

46. (d): Hint: T = 2π 2

kkk/m '

eq = for v′ < v.

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