50 MCQ of Physics

MULTIPLE CHOICE QUESTIONS

1. A hollow metal sphere of radius 15 cm is charged such that the potential on its surface is 20 V. The potential at the centre of the sphere is

a. 20 V

b. 30 V

c. 5 V

d. 0 V

Sol: Correct option is (a)

For a hollow metal sphere the potential at centre of sphere is equal to the potential on the surface of the sphere. Therefore potential at the centre of sphere is 20 V.

2. A uniform electric field having a magnitude E and direction along the positive y-axis exists. If the potential V is zero at y=0, then its value at y=+y will be

a. yE

b. 2yE

c. –yE

d. -2yE

Sol: Correct option is (c)

We know that 0oV

Also yV is potential at y=+y then o y yV V yE V yE

3. An electric dipole of momentum oP is placed in the position of stable

equilibrium in uniform electric field of intensity oE . The couple required to rotate it through angle from the initial position is

a. o oP E

b. sino oP E c. 2 o oP E

d. 2 sino oP E

Sol: Correct option is (b)

Couple = sinoqE a

Where oq a P

Couple required = sino oP E

4. A given charge oQ is situated at a certain distance from an electric dipole

in the end on position, experiences a force oF . If the distance of charge is

halved the force acting on the charge oQ will be

a. F

b. 2F

c. 3F

d. 8F

Sol: Correct option is (d)

Electric field at a distance 3

2Kpr

r

Hence force at a distance 3

2Kpr Q F

r

Also force at a distance 2

ron charge Q =

2

28

2

KpQ F

r

Hence if distance of charge is halved force acting = 8 <Li><span>*

5. xyz is an equilateral triangle. Charges -2q are placed at each corner. The electric intensity at A will be

a. 2

2

1 2

4 o

q

r

b. 2

1

4 2o

q

r

c. 0

d. 21

4 2o

q

r


Electric intensity at A is

Where E = 1 ( 2 )

4 o

q

r

120 12 cos 2 0

2 2

0

net

net

E E E E E

E

6. Work done in carrying a charge q one around the circle of radius R with a charge Q at the centre is

a. 2

1

4 o

qQ

r

b. 0

c. 21

4 o

q Q

r

d. 2

2

1

4 o

qQ

r


The force acting perpendicular to the displacement of the charge.

Hence work done = 0

7. Two conducting spheres of radii 1R and 2R are at the same potential. The ratio of their charges is

a. 1 2R R

b. 2

1

R

R

c. 2

1

2

R

R

d. 1

2

R

R


Potential of sphere 1, 11

1

1

4 o

QV

R


2

1

4 o

QV

R

As 1 2V V

1 2

1 2

1 1

4 4o o

Q Q

R R

1 1

2 2

Q R

Q R

8. An electric cell does 25 joules of work in carrying 5 coulombs charges around the close circuit. The electromotive force at the cell is

a. 3 volts

b. 8 volts

c. 5 volts

d. 9 volts


Electromotive force = 25

5arg 5

Work Joulesvolts

Ch e coulombs

9. Two conducting spheres of radii 1R and 2R are at the same chartged. The ratio of their potential is

a. 1 2R R

b. 2

1

2

R

R

c. 2

1

R

R

d. 2

12

2

R

R



1

1

4 o

QV

R


2

1

4 o

QV

R

As 1 2Q Q

1 2

2 1

V R

V R

10. Two conducting spheres of radii 1R and 2R have same electric field near their surface. The ratio of their electric potential is

a. 2 1R R

b. 2 22 1R R

c. 2

1

R

R

d. 1

2

R

R


Electric field of sphere 1, 1 11 2

1 1

1

4 o

Q VE

R R

Electric field of sphere 2, 2 22 2

2 2

1

4 o

Q VE

R R

As 1 2E E

1 2

1 2

V V

R R

1 1

2 2

V R

V R

11. If the force exerted by a small spherical charged object on another charged object at 8 m is 5 N, what will be the force exerted when the second object is moved to 16 m.

a. 3 N

b. 2 N

c. 2.25 N

d. 1.25 N


F= 1 22

1

4 (8)o

q q

Also F=5

1 22

15

4 (8)o

q q

Now 1 22

11.25

4 (16)o

q q

N

12. If the force of an electric file don 10 coulomb charge is 25 N, The intensity of field is

a. 3 N/C

b. 2.5 N/C

c. 3.8 ev

d. 2.5 ev


Electric filed intensity = arg

Force

ch e

= 25

10

N

Coulomb= 2.5 N/C

13. Two plates are 2 cm apart and the potential difference between them is 200 volts. The electric field intensity between the plates is

a. 300 N/C

b. 100 N/C

c. 10000 N/C

d. 1000 N/C


Electric field intensity = V

d

V= 200 Volts

d= 22 10 m

2

20010000

2 10E

N/C

14. Electrons are caused to fall through a potential difference of 250 volts. If they were initially at rest, their final speed is

a. 69.37 10 /m s

b. 68.24 10 /m s

c. 75.9 10 /m s

d. 89.91 10 /m s


21

2 e em v eV

19

31

12

6

2

2 1.6 10 250

9.1 10

80010

9.1

9.37 10 /

ee

e

e

e

eVv

m

v

v

v m s

15. The capacitors of a parallel plate condenser does not depend upon

a. medium between plates

b. distance between plates.

c. area of plates

d. metal of plates.


Capacitance = o A

d

Capacitance is independent of metal of plates of conductor.

16. In a charged capacitor, the energy is stored in

a. metal plates of capacitor

b. positive charges

c. negative charges

d. filed between the plates


Energy is stored in the form of field present between the plates.

17. Which of the following relations is correct?

a. 2q

VC

b. q CV

c. 1qCV

d. C

qV


If q is the charge on the body and V is potential then

Capacitance q

CV

q CV

18. The capacitance of the parallel plate condenser is given by

a. C

VQ

b. odC

A

c. o AC

d

d. o

dC

A


tan odCapaci ce

A

Where o = constant

A= Area of plates

d= distance between the plates.

19. The capacitance of a parallel plate condenser is oC . Its capacity when the separation between the plates is doubled will be

a. 2 oC

b. 3 oC

c. 3

oC

d. 2

oC


Capacitance = oo

dC

A

When ' 2d d

'' 2 2

o o oA A CC

d d

20. Two condensers of capacitance 1C and 2C respectively are connected in parallel. The equivalent capacitance of system is

a. 1 2C C

b. 21 1C C

c. 1 2C C

d. 1

2

C

C


1 2eqC C C

Equivalent capacitance is equal to the summation of capacitance of each capacitor connected in parallel.

21. Two condensers of capacitance 1C and 2C are connected in series. The equivalent capacitance of the system is

a. 1

2

C

C

b. 1 2

1 2( )

C C

C C

c. 2

1

C

C

d. 1 2C C

Sol: Correct option is (b)When two condensers are connected in parallel then let eqC be their equivalent capacitance

1 2

1 1 2

1 1 1eq

eq eq

C CC

C C C C C

22. A condenser of capacity 30 F is charged to 20 volts. The energy stored in the condenser is

a. 36 10 joules

b. 48 10 joules

c. 39 10 joules

d. 317 10 joules


Energy stored = 21

2C V

6 2

6

6

130 10 (20)

21

30 400 102

6000 10

36 10 joules

23. A 30 F capacitor has charge on each plate 36 10 coulomb, and then the energy stored is

a. 430 10 joules

b. 225 10 joules

c. 387.5 10 joules

d. 260 10 joules


Q= 36 10 coulomb

C= 630 10 F

We know that

Energy = 21

2CV

Also Q=CV3

6

6 10

30 10

QV

C

200V volts

Energy = 21

2CV

6 4

6 2

130 10 4 10

21

30 10 (200)2

260 10 joules

24. Two capacitors 6 F and 3 F are connected in series, the effective capacitance of the system will be

a. 3 F

b. 2 F

c. 6 F

d. 1 F


1 1 1

6 3eqC F F

126

6

6 3 102 10

9 102

eq

eq

C F

C F

25. If a 6 F condenser is charged to 100 volts and its plates are connected by a wire, the heat produced in the wire is

a. 38 10 joules

b. 23.8 10 joules

c. 23 10 joules

d. 27.6 10 joules


Heat produced = Energy stored in condenser

= 21

2CV

6 216 10 (100)

2

23 10 joules

26. Two capacitors each of capacitance 2 F are connected in parallel. To this combination, a third capacitor of capacitance 4 F is connected in series. The equivalent capacitance of the system is

a. 2 F

b. 7 F

c. 12 F

d. 8.3 F


1 1 1

2 2 4

4 4

8

eq

eq

C F F F

F FC

F

2eqC F

27. A condenser is charged through a potential difference of 100 volts possesses charge of 0.2 coulomb, when the condenser of discharged it would release an energy

a. 1 joules

b. 8 joules

c. 7 joules

d. 10 joules


V = 100 volts Q = 9.2 coulomb

We know that Q = CV

30.22 10

100

QC C F

V

Now energy released = 21

2CV

3 212 10 (100) 10

2 joules

28. A parallel plate capacitor has a capacitance of 30 F in air and 45 Fwhen immersed in another medium. The dielectric constant K of the medium is

a. 2

b. 1.5

c. 2.8

d. 3.5


oair

omedium

AC

dA

C Kd

451.5

30medium

air

C FK

C F

29. How many number of electrons are to be put on a spherical conductor of radius 0.3 m to produce an electric field of 0.012 N/C just above its surface

a. 56 10

b. 47.2 10

c. 57.5 10

d. 0


Electronic field just above the surface of spherical conductor

9

2 2

9 10

(0.3)

KQ QE

r

9

2

11

14

20

5

9 10 ( )0.012

9 10

0.012 10

12 10

16 10

7.5 10

ne

ne

n

n

30. What is the angle between the electric dipole moment and the electric field strength due to it on the axial line?

a. 30o

b. 0o

c. 60o

d. 90o


Both of the dipole moment and electric field are in same direction, hence the angle between them is 0o

31. What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

a. 180o

b. 60o

c. 30o

d. 90o


On equatorial line the electric field strength is in the opposite direction to that of electric dipole moment, hence angle between them is 180o .

32. Three charges 1C, -2C, 1C are placed at three vertices of an equilateral triangle. Which of the statements is true for the centre O of triangle?

a. At O field and potential both are zero.

b. At O field is non-zero but potential is zero.

c. At O field and potential both are non-zero.

d. At O field is zero but potential is non-zero.


At O potential due to three charges is zero but there exists a net electric field.

33. 64 identical drops of mercury are charged simultaneously to the same potential of 5 units. Assuming the drops are made to combine to form one large drop, then its potential is

a. 40 units

b. 10 units

c. 15 units

d. 80 units


Let radius of small drops be r and that of a big drop is R, then

3 34 464

3 34

r R

R r

Let potential of small drops = 1

4 o

q

r

Also 1

54 o

q

r

units

Then potential of big drop 1 64

4 4

5 16o

q

r

80 units

34. Two particles of masses M and 3M with charges q and q are placed in an uniform electric field E and allowed to move for same time. The ratio of their kinetic energies will be

a. 1:2

b. 2:1

c. 3:1

d. 1:3


For particle 1 1

qEa

M

For particle 2 2 3

qEa

M

1 22a a

Also 2 2 21 1 1

1 1( )

2 2K M a t Ma t

and 2 2 22 2 2

1 13 ( ) 3

2 2K M a t Ma t

2 21 1 2

2 22 2 2

9 3

3 3 1

K Ma aM

K Ma M a

35. When two capacitors one of 4 F and other 8 F are connected in series and the combination is charged to a potential difference of 90 volts. The potential difference across 4 F capacitor is

a. 70 volts

b. 60 volts

c. 10 volts

d. 90 volts


Let 1 4C F and 2 8C F

Also let 1V is potential difference across 1C and 2V is potential difference across

2C

1 1 2 2 1 2

1 2

4 8

2

C V C V V F F V

V V

Also 1 2

2

2

90

3 90

30

V V

V

V

1 60V volts

36. Ten capacitors each of capacitance 1 F are to be connected to obtain a

capacitance of 9

10F . Which of the following combination is correct.

a. 5 in series 5 in parallel.

b. 3 in series and 7 in parallel.

c. 9 in parallel and 1 in series.

d. All 10 in series.


1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 101

9 9

eq

eq

C

C

9

10eqC F

37. In order to obtain a time constant of 5 seconds in a RC circuit containing a resistance of 200 the capacity of a condenser should be

a. 0.75 F

b. 0.1 F

c. 0.625 F

d. 0.025 F


T=RC= 5

200 x C = 5 5 1

200 40C

0.025C F

38. A 6 F capacitor is charged to 100 volts and then its plates are joined through a resistance of 2 K . The heat produced in the resistance is

a. 23 10 joules

b. 36 10 joules

c. 28 10 joules

d. 37 10 joules


Heat produced = Energy stored in the capacitor

2

6 2

1

21

6 10 (100)2

CV

23 10 joules

39. The resistance of a wire of uniform radius R and length l is x. the resistance of another wire of same material but radius 2R and length 2l will be

a. 2x

b. 3x

c. 2

x

d. 3

x


2

'2 2

2 1

(2 ) 2 2

lx

R

l l xx

R R

40. Two resistances 1R and 2R are connected in series and resistance

3R is connected in parallel to this series connection. The equivalent resistance of the combination will be

a. 1 2 3R R R

b. 1 2

3

( )R R

R

c. 1

2 3( )

R

R R

d. 1 2 3

1 2 3

( )R R R

R R R


Equivalent of series connection = 1 2R R

1 2 3

1 1 1

eqR R R R

1 2 3

1 2 3

( )eq

R R RR

R R R

41. The resistance of a wire is R . The wire is stretched to double its length. What is the new resistance of wire in ohm?

a. 3R

b. R

c. 8R

d. 4R


lR

A

' 2l l

Now we know that volume of wire is constant, therefore

' ' ' '

'

''

(2 )2

(2 )4

2

AAl Al Al A l A

l lR R

AA

42. When a d.c. battery of emf V and internal resistance R delivers

maximum power to an external resistance 'R , then ratio '

R

R equals

a. 1

b. 2

c. 4

d. 3


For the battery to deliver maximum power the internal resistance should be

equal to the external resistance, hence ''

1R

R RR

43. A current of 3.2 A is flowing in a conductor. The number of electrons flowing per second through the conductor will be

a. 178 10 electrons

b. 192 10 electrons

c. 194 10 electrons

d. 193.5 10 electrons


Current = 3.2Q

At

Q= 3.2 coulombs

191.6 10 3.2n C

192 10n electrons

44. The resistance of 10 cm long wire is 2 ohm. The wire is stretched to uniform wire of 20 cm length. The resistance of stretched wire will be

a. 6 ohm

b. 4 ohm

c. 8 ohm

d. 10 ohm


LR

A

Here

'

1

2

2

L l

AA

1 '4 4 2 8R R R ohm

45. Three 5 ohm resistors are connected to form a triangle. The resistance between any two corners is

a. 5

3ohm

b. 8 ohm

c. 10 ohm

d. 10

3ohm


1 1 1 1 1

5 5 5 10 5eqR

1 15 50 10

50 15 3eqeq

RR

ohm

46. A battery of 10 volts is connected to the terminals of a 5 meter long wire of uniform thickness and resistance of the order of 1000 ohm. The difference of potential difference between two points separated by 1 m on the wire will be

a. 2 volts

b. 5 volts

c. 3 volts

d. 7 volts


Potential gradient = 10

2 /5

voltsv m

m

Potential difference between two points 1 m apart = 2 v/m x 1 m = 2 volts

47. A wire has resistance of 3 . A second wire of same material is having length half and radius of cross section half that of the wire. The resistance of second wire is

a. 4

b. 1.5

c. 3

d. 6


23

L lR

A r

Now '

2

ll and '

2

rr

'2 2

2 2 3 2 6

2

l lR

rr

48. A wire has resistance 16 ohms. It is bent in the form of a circle. The effective resistance between the two points on any diameter of the circle is

a. 2 ohms

b. 8 ohms

c. 4 ohms

d. 16 ohms


When wire of 16 ohms is bent in the form of a circle, then the resistance of circle, then the resistance of semicircle is 80 ohms.

8 8 644

8 8 16eqR

49. The smallest resistance which can be obtained by connecting 100 resistances of 2 ohm each is

a. 4 ohms

b. 1

50 ohms

c. 50 ohms

d. 200 ohms


Equivalent resistance is smallest when all the resistance are connected in parallel. For parallel connection

2 1

100 50eqR

50. A cell of negligible resistance and e.m.f. of 30 volts is connected to series combination of 6,3 and 1 ohm resistance. The potential difference in volts between the terminals of 1 ohm resistance is

a. 6 volts

b. 8 volts

c. 3 volts

d. 18 volts


Current = 30

36 3 1

A

Potential difference across 10 ohm = 3 A x 1 Ohm = 3 volts

50 MCQ of Physics

Documents

o r1 potential of sphere

electric potential

o r2 v1 r2 v2 r1

o r2 q1 r1 q2 r2

r2 r1 r1 r2correct option

r2 electric field of

potential v

c v correct option