Suggested Solutions for 2011 J1 H2 Physics Paper 1 1. A B ...

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Suggested Solutions for 2011 J1 H2 Physics Paper 1 1. Which of the following is a unit of pressure?

A kg m s-1

B kg m-1 s-2

C kg m2 s-2

D kg m-2 s-1

Ans [B]

Solution P = Force/area Units of pressure, P = (kg m s-2) / m2 = kg m-1 s-2

2. Which of the following is not equal to 6.02 x 10-10 C?

A 602 pC

B 60.2 nC

C 6.02 x 10-4 C

D 6.02 x 10-13 kC

Ans [B]

Solution A 602 pC = 602 x 10-12 = 6.02 x 10-10 C B 60.2 nC = 60.2 x 10-9 = 6.02 x 10-8 C [Wrong]

C 6.02 x 10-4 C = (6.02 x 10-4)x10-6 = 6.02 x 10-10 C D 6.02 x 10-13 kC = (6.02 x 10-13) x 103 = 6.02 x 10-10 C

3. Four students measured and calculated the elementary charge, e. The table shows the results obtained. Which student obtained a set of results that could be described as accurate and precise? [e = 1.60 x 10-19 C]

Student Electronic charge, e / 10-19 C

A 1.62 1.59 1.59 1.61 1.60

B 1.57 1.63 1.64 1.58 1.59

C 1.59 1.60 1.58 1.57 1.57

D 1.58 1.62 1.65 1.59 1.66

Ans

[A] Solution A lavg = 1.602, range = 1.62 – 1.59 = 0.03 B lavg = 1.602, range = 1.64 – 1.57 = 0.07 C lavg = 1.582, range = 1.60 – 1.57 = 0.03 D lavg = 1.620, range = 1.66 – 1.58 = 0.08 Hence, [A] is accurate (average close to TRUE value) & precise (small range/scatter)

4. Which pair includes a vector quantity and a scalar quantity?

A displacement, acceleration

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B work, potential energy

C power, time

D force, kinetic energy

Ans [D]

Solution A Both vector quantities B Both scalar quantities C Both scalar quantities

5. The diagram below shows a vector of magnitude F and two of its components of magnitudes F1 and F2. These components are at right angles to each other. Which of the following statements is true?

A F F F 1 2

B F = F2 sin

C 2 2

1 2F F F

D F2 = F cos

Ans [C]

Solution Use of vector addition

6. A motorist travelling at 15 m s-1 approaches traffic lights which turn red when he is 12 m

away from the stop line. His reaction time is 0.10 s and the car can be brought to rest with a uniform deceleration in 1.2 s when the brakes are applied. If he brakes fully, how far from the stop line will he stop?

A 1.5 m

B 2.3 m

C 3.0 m

D 4.5 m

Ans [A]

Solution Using v = u + at 0 = 15 + a(1.2) a = - 12.5 m s-2

Distance traveled during reaction time = 15 x 0.1 = 1.5 m Using v2 = u2 + 2as

0 = (15)2 + 2(-12.5)(s) s = 9.0 m

Total distance traveled = 1.5 + 9.0

F

F2

F1

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= 10.5 m Distance from stop line = 12 – 10.5 = 1.5 m

7. At a height of 120 m from the ground, a loose bolt detaches from the rocket when it is travelling vertically upwards at 10.0 m s-1. Calculate the time taken for the bolt to strike the ground.

A 4.0 s

B 4.9 s

C 6.1 s

D 12 s

Ans [C]

Solution Using s = ut + ½ at2 -120 = 10.0 (t) + ½ (-9.81)(t)2 t = 6.1 s

8. A stone is thrown vertically upwards. A student plots the variation with time of its velocity.

What is the vertical displacement of the stone from its starting point after 5 seconds?

A 15 m

B 20 m

C 25 m

D 65 m

Ans [C]

Solution Area under v-t graph = displacement Displacement of stone = ½ x 30 x 3 + ½ (–20) (5 – 3) = 25 m

9. A toy rocket is launched vertically from Earth with a constant acceleration. After some time, the fuel is used up and the toy rocket falls freely back to Earth. Which of the following velocity-time graphs best represents the journey?

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Neglect air resistance.

A

B

C

D

Ans [A]

Solution Initially the toy rocket accelerates uniformly. Hence the velocity of the rocket should increase (hence B and D are wrong). When the fuel is used up, the rock still move upwards due to its inertia. However it is moving upwards with decreasing velocity until it reaches the maximum height (velocity = 0 m s-1). After which it will move downwards and fall back to Earth. Hence there should be both positive and negative velocity shown in the v-t graph.

10. A tennis ball is released from rest at the top of a tall building. Assuming air resistance is significant, which graph best represents the variation with time t of the acceleration a of the ball as it falls?

A

B

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C

D

Ans

[D] Solution When the ball is released (at t = 0), the ball's acceleration is g. So answer B and C is eliminated. As air resistance is not negligible, the acceleration of the ball will not be constant (cannot be answer A). Instead, the acceleration of the ball will decrease to zero after some time ( the point where terminal velocity has been attained )

11. The force-extension graph of a spring is shown in the figure below.

The work done in extending the spring from x1 to x2 is given by

A ½(F1 + F2) (x2 – x1)

B ½(F2 + F1) (x2 + x1)

C ½(F2 - F1) (x2 - x1)

D F2x2 - F1 x1

Ans A

Solution Work done = area under the graph = trapezium area for the straight line

12. Two springs P and Q both obey Hooke’s Law. They have spring constants 2k and k respectively. The springs are stretched separately by the same force. The elastic potential energies stored in springs P and Q are WP and WQ

respectively. How is WP related to WQ?

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A WP = ¼ WQ

B WP = ½ WQ

C WP = 2 WQ

D WP = 4 WQ

Ans B

Solution By Hooke’s Law, F = k x

For spring P, F = (2k) xP

xP = F

2k

For spring Q, F = (k) xQ

XQ = F

k

Work done on spring: W = ½ F x Since F is constant,

W x

1

2

P P

Q Q

P

Q

W x

W x

FW 2k

FW

k

WP = ½ WQ

13. The given diagram shows a column of dry air trapped by mercury in a narrow test tube.

Which graph best shows how the length l of the air column varies with the angle of the tube to the vertical?

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A

B

C

D

Ans B

Solution

When = 0, the force on the trapped air is maximum, hence the trapped air is most compressed, hence l is minimum.

14. A student makes some observations of a ball falling through identical beakers of fluids with different viscosity after it is released in each of them. Which of the following observations could be used to identify the most viscous fluid?

A The ball initially moves with the largest acceleration.

B The ball takes the longest time to reach constant speed.

C The maximum displacement of the ball is the same.

D The ball moves at the smallest constant speed.

Ans D

Solution A is wrong. - This depends on upthrust which depends on density, not viscosity. B is wrong. - In the more viscous fluid, the ball experiences higher drag force. Thus it will reach the equilibrium state earlier. C is wrong. - The maximum displacement is constrained by the beaker depth instead of depending on the fluid viscosity. D is correct. - At terminal velocity, the weight of the ball is balanced by the drag force. The more viscous fluid has a higher drag force at the same velocity. Thus to balance the same weight, the ball moving through a more viscous fluid would have a smaller terminal velocity.

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15. In 2001, the leaning tower of Pisa was stabilized by a bundle of steel cable anchored to the ground as shown by the simplified sketch below.

The weight of the tower is W, the tension in the cable is T and the reaction from the ground is R.

Which vector triangle best represents the forces acting on the tower?

A

B

C

D

AnsD

Solution R must be normal to the base – A, B wrong Horizontal component of T must be leftward – B & C wrong

16. Two blocks, X and Y of masses m and 2m respectively, are accelerated along a smooth

horizontal surface by a force F applied to block X as shown in the diagram below.

Tower

Steel Cable

Ground

T

R W

T

R W

T

R

W

T

R

W

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What is the magnitude of the force exerted by block Y on block X during this acceleration?

A 0

B F

3

C 2F

3

D F

Ans C

Solution FBD of X & Y

(3 )3

FF m a a

m

FBD of X OR FBD of Y

2

3 3

YonX

YonX

F F ma

F FF F m

m

2

22

3 3

2

3By N3L,

XonY

XonY

YonX

F ma

F FF m

m

FF

17. A space-research rocket stands vertically on its launching pad. Prior to ignition, the mass

of the rocket and its fuel is 1.7 x 103 kg. On ignition, gas is ejected from the rocket at a speed of 2.5 x 103 m s-1 relative to the rocket, and the fuel is consumed at a constant rate of 7.4 kg s-1. Calculate the resultant force acting on the rocket on ignition.

A 1.82 x 103 N

B 1.67 x 104 N

C 1.85 x 104 N

D 3.52 x 104 N

Ans A

Solution 3

4

4

4 3 3

( ) 7.4(2.5 10 0)1.85 10

1

1.85 10

Re 1.85 10 (1.7 10 )(9.81) 1.82 10

on

on rocket gas

N

By N3L, N

N

gas by rocket

by

m v uF

t

F

sult F

18. A ball falls vertically and bounces on the ground. The following statements are about the

forces acting while the ball is in contact with the ground. Which statement is correct?

A The force that the ball exerts on the ground is always equal to the weight of the ball.

Y X F

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B The force that the ball exerts on the ground is always equal in magnitude and opposite in direction to the force the ground exerts on the ball.

C The force that the ball exerts on the ground is always greater than the weight of the ball.

D The weight of the ball is always equal and opposite to the force that the ground exerts on the ball.

Ans B

Solution By N3L, the force by the ball on the ground is always equal in magnitude but opposite in direction to the force by the ground on the ball

19. The diagram shows two trolleys, X and Y, about to collide and gives the momentum of

each trolley before the collision.

After the collision, the directions of motion of both trolleys are reversed and the magnitude of the momentum of X is then 2 N s. What is the magnitude of the corresponding momentum of Y?

A 6 N s

B 8 N s

C 10 N s

D 30 N s

Ans C

Solution By conservation of linear momentum, 20 + (-12) = pY + (- 2) pY = 10 N s

20. Three identical stationary discs, P, Q and R are placed in a line on a horizontal, flat and

frictionless surface. Disc P is projected straight towards disc Q.

If all consequent collisions are perfectly elastic, what will be the final motion of the three discs?

P Q R

A moving left moving left moving left

B stationary stationary moving left

C stationary stationary moving right

D moving right moving right moving left

Ans Solution

P Q R

X Y

12 N s 20 N s

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C Since all collisions are perfectly elastic, there is a complete transfer of KE from disc P to Q and Q to R. Only disc R will be moving towards the right after the collision while disc P and Q will remain stationary.

21. Ball X slides down a frictionless slope while Ball Y falls freely from the same height. Both

balls are initially at rest and the gradient of the slope is vertical at the starting position of X as shown below.

Which ball has a higher speed after moving through the same height H?

A X

B Y

C X and Y will have the same speed

D X or Y, depending on which is heavier

Ans C

Solution Using conservation of energy, For Ball X, PETop + KETop = PEbottom + KEbottom mXgH + 0 = 0 + 1/2mXvX

2 vX

2 = 2gH For Ball Y, PETop + KETop = PEbottom + KEbottom mygH + 0 = 0 + 1/2myvy

2 vy

2 = 2gH Hence, both balls will have the same speed after falling through the same height H.

22. A body is projected at an angle above the horizontal with a given speed. Air resistance may be taken as negligible. Which one of the following statements is correct?

A The kinetic energy of the body is a maximum at the maximum height attained.

B The potential energy of the body increases uniformly with time during ascent.

C The total energy of the body is constant throughout the motion.

D The momentum of the body is constant throughout the motion.

Ans Solution

H

X Y

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C The total energy of the body is constant throughout the motion. With negligible air resistance, the total energy of the body is constant.

23. A 1.0 kg mass, with an initial kinetic energy of 20 J, moves up a smooth slope as shown

below.

What is the speed of the mass after it has moved a distance of 2.0 m? A 0 m s-1

B 5 m s-1

C 10 m s-1

D 20 m s-1

Ans B

Solution PETop + KETop = PEbottom + KEbottom (1.0)(9.81)2sin30o + KETop = 0 + 20 KETop = 10.2 J 1/2mv2 = KETop = 10.2 J v2 = 20.4 v = 4.51 m s-1

30°

2.0 m

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24. A mass hanging on a spring oscillates vertically between X and Z. Its equilibrium

position is at Y. The spring has negligible mass. Which of the following gives the correct description of energy and force?

Elastic potential energy of spring is minimum

when mass is at

Largest net upward force acts on mass when it is at

A Z Y

B X Z

C X Y

D Z Z

Ans

B Solution Elastic potential energy When the mass it at X, the spring should have the least extension. Hence, the EPE would be the minimum at X. Net upward force Throughout the oscillation, the tension in the spring would be the highest when the mass is at Z while the weight of the mass remains constant. The net upward force would be the highest based on these 2 forces acting on the mass.

X

Y

Z

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25. A toy car of mass 2.0 kg is travelling at constant speed for 5.0 s. The car engine is

providing 160 W of useful power and driving force on the car is 80 N. At what speed does it travel?

A 0.5 m s-1

B 1.0 m s-1

C 2.0 m s-1

D 4.0 m s-1

Ans C

Solution Using Power = Force x Constant Velocity Velocity = Power / Force = 160 / 80 = 2.0 m s-1

26. The temperatures of two beakers of water of different amounts are measured using the

same thermometer. The temperatures registered are both 32 C and are steady.

The water in one beaker is then poured into the other beaker.

Assume no heat loss during pouring, which one of the following statements is correct?

A The final temperature of the water will be less than 32 C since beaker B has

less energy. B The final temperature of the water will be more than 305.15 K since beaker A

has more energy. C Since the mass and the specific heat capacity of water are unknown, the

temperature of the water cannot be determined. D The water from beaker B will be at thermal equilibrium with the water from

beaker A. Ans: D

Thermal equilibrium 27. A small quantity of water of mass m at a temperature (in oC) is poured on to ice of

mass M which is at its melting point (M >> m).

Beaker A Beaker B

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If c is the specific heat capacity of water and L the specific latent heat of fusion of ice, then the mass of ice melted is given by

A ML

mc

B

Mc

L

C

mc

ML

D

mc

L

Ans: D

mc ( 0) = mice L mice =mc

L

28. The graph shows the variation of temperature T against time t of a certain substance

which was originally a liquid at t = 0 s. Heat was removed from it at a constant rate until it became a solid.

Which one of the following could be correct? Specific heat capacity of liquid

/ J kg1 K1

Specific heat capacity of solid

/ J kg1 K1

A 1500 3000

B 1800 900

C 2500 2500

D 4500 3000

Ans: B

Pt = mc

For liquid: P (100 ) = mcliq (400 300 ) - - - - - (1)

0 50 100 150 200 250 t / s

T / K

400

300

200

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For solid: P ( 50 ) = mcsol (300 200 ) - - - - - (2)

(1)

(2):

100

50=

liq

sol

c

c= 2 cliq = 2csol

29. The expansion of a mass m of an ideal gas at a constant pressure P is shown by line

B in the volume-temperature graph below.

Which line shows the expansion of a mass 2

m of the same gas, at a pressure of

4

P ?

Ans: A

pV = nRT V

T=

nR

p gradient =

4

T (line B)

For the new situation: 2

V

T

= 2

4

n

p

R gradient =

8

T (line A)

30. When the pressure of a fixed mass of ideal gas is doubled by heating at constant

volume, A the number of molecules per unit volume doubles. B the mean square speed of the molecules doubles. C the density of the gas doubles. D the temperature of the gas remains constant. Ans: B

pV = nRT - - - - - (1) 2pV = nRT2 - - - - - (2)

(2)

(1): 2 = 2T

T T2 = 2T

Since 12

m<c2> T

When T is doubled, <c2> is also doubled.

Volume

Temperature

A

B

C

D

8

4

2

1