Physics

Single correct answer type:

1. Two flatworms climb over a very thin wall, high. One of the worm is long,

the other is wider and only long. Which of the following statement is correct regarding

them?

(A) worm has done more work against gravity

(B) 1 worm has done more work against gravity

(C) Both worms have done equal work against gravity

(D) Ratio of work done by both the worms is

Solution: (B)

The work done against gravity can be calculated from the increases in height of the centre of

mass. The centre of mass of a worm folded in two is located at the middle of either half, i.e. at a

point one-quarter of the worm's total length from one end, as given in the figure below:

Thus, the centre of mass of the narrow flat worm travels up the wall; while that of the

broad one moves . Hence, work done by worm is more against gravity. Also, the

ratio of the work done is .

2. A rocket is intended to leave the Earth’s gravitational field. The fuel in its main engine is a

little less than the amount that is necessary and an auxiliary engine, (only capable of operating

for a short time) has to be used as well. When is it best to switch on the auxiliary engine?

(A) At take-off

(B) When the rocket has nearly stopped with respect to the Earth.

(C) It doesn’t matter.

(D) Can’t say

Solution: (A)

The rocket has to reach the highest possible total energy. If the zero level of gravitational

potential energy is 'infinitely' far away, then the energy of the rocket standing on the surface of

the earth is negative. The energy released during the operation of the engines increases the

total energy of the rocket, and the rocket can leave, the earth's gravitational field if the sum of

its potential and kinetic energies becomes positive.

The energy released in the course of the operation of the principal and auxiliary engines

increases the total energy of the rocket and its ejected combustion products by a fixed value;

this increase is independent of the moment when the engines are scratched on. However, the

speed at which the combustion products fall back to the earth does depend on the timing of

the rocket's e operations. Indeed, if the auxiliary engine starts working when the rocket is at a

greater height, the combustion products fall further and their speed and total energy are higher

when they hit the ground. This means that the sooner the auxiliary engine is switched on, the

higher the energy ultimately acquired by the rocket. The same argument is valid for the

principal engine, and if the only energy consideration apply, it is best to operate the engines for

the shortest time and at the highest thrust.

3. The turns of a solenoid, designed to provide a given magnetic flux density along its axis, are

wound to fill the space between two concentric cylinders of fixed radii. How should the

diameter of the wire used be chosen so as to minimize the heat dissipated in the windings?

(A) Wire should be multiple of

(B) Wire should be multiple of ⁄

(C) Wire is independent of

(D) Can’t say

Solution: (C)

The cross-sectional area of the space to be filled is fixed, whilst that of the wire varies as .

Thus, . The resistance of one turn is inversely proportional to the cross-sectional area

of the wire, i.e. varies as and hence the resistance per unit length of the solenoid is

. The flux density is and therefore the required current .

The heat dissipated per unit length is , which ( ) , i.e. independent of . Thus,

within limits, it does not matter what diameter wire is chosen so far as the heating effect is

concerned.

4. A cylindrical tube of uniform cross-sectional area is fitted with two air tight frictionless

pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the

gas is and temperature is , atmospheric pressure is also . Now, the temperature of the

gas is increased to , the tension of wire will be

(A)

(B)

(C)

(D)

Solution: (B)

Volume of the gas is constant i.e. constant

i.e. pressure will be doubled if temperature is doubled.

Let be the tension in the wire. Then, equilibrium of any one pipes gives.

( ) ( )

5. A particle of mass is executing oscillation about the origin on -axis. Its potential energy is

( ) | | . Where is a positive constant. If the amplitude of oscillation is , then its time

period is proportional to

(A) √ ⁄

(B)

(C) √

(D) ⁄

Solution: (A)

Given,

Total energy ( ) Maximum potential energy

From conservation of energy

(

)

(

)

( )

√

( )

√ √

or Integrating ∫

√ √

∫

⁄

or ∫

√ √

Let

∫

√ ( )

⁄

√

6. A body is projected vertically upwards. The times corresponding to height while ascending

and while descending are and , respectively.

Then, the velocity of projection will be (take as acceleration due to gravity)

(A) √

(B) ( )

(C) √

(D)

( )

Solution: (B)

Let be initial velocity of vertical projection and be the time taken by the body to reach a

height from ground.

Here,

Using,

, we have

( )

√

√

It means has two values, i.e.

√

√

( )

7. A long straight wire is carrying current in direction. The plane contains a

closed circular loop carrying current and not encircling the straight wire. The force on the

loop will be

(A) ⁄

(B) ⁄

(C) Zero

(D) Depends on the distance of the centre of the loop from the wire

Solution: (D)

Situation is shown in the figure given below

Thus, the force depends on the distance of the centre of the loop from the wire.

8. When the radioactive isotope decays in a series by emission of three alpha ( )

and a beta ( ) particle, the isotope which remains undecay is

(A)

(B)

(C)

(D)

Solution: (A)

Due to emission of particles, the mass number is reduced by 12 while atomic number is

decreased by 6. Due to emission of particle, the atomic number is increased by one while

there is no change in mass number. Now, resulting mass will be decreased by 12 and atomic

number is decreased by 5. So, isotope .

9. A solid cylinder is attached to a horizontal massless spring as shown in figure. If the

cylinder rolls without slipping, the time period of oscillation of the cylinder is

(A) √

(B) √

(C) √

(D) √

Solution: (C)

Let be the extension in the spring,

Then,

Torque acting on the cylinder about point of contact,

( )

√

√

√

10. lamps each of resistance , are fed by a machine of resistance . If light emitted by

any lamp is proportional to the square of the heat produced, prove that most efficient way of

arranging them is to place them in parallel arcs, each containing lamps, where is

the integer nearest to

(A) (

) ⁄

(B) (

) ⁄

(C) ( ) ⁄

(D) ( ) ⁄

Solution: (B)

As each are containing lamps, hence,

Resistance of each arc

Number of arcs ⁄

Total resistance is given by

(

)

Total resistance ( )

If is the emf of the machine, current entering the arcs is ( )⁄ and in each arc is

( )⁄ .

Hence, current passing through each lamp

( ⁄ )

[

]

Now, heat produced per second in the lamps is

Since, light emitted is proportional to therefore light produced is maximum when and

hence is maximum or *

+ is minimum. Hence, we can write,

0(

) ⁄

(

) ⁄

1

(

) ⁄

The is minimum when √ ⁄ √ ⁄ or very small or is closely equal to ( ⁄ ) ⁄ .

11. Radioactive decay will occur as follows

Half life

Half life

Half life

If a certain mass of radon ( ) is allowed to decay in a certain container; then after 5

minutes the element with the greater mass will be

(A) Radon

(B) Polonium

(C) Lead

(D) Bismuth

Solution: (C)

Let be initial mass of

Number of half-lives of in 5 minutes

( ) (

)

The mass converted into ( ⁄ )

Number of half-lives of in minutes

Mass of left (

)

This means that formed will soon decay to lead. Hence, lead will have maximum

mass nearly (

)

12. A stream of a liquid of density flowing horizontally with speed rushes out of a tube of

radius and hits a vertical wall nearly normally. Assuming that the liquid does not rebound

from the wall, the force exerted on the wall by the impact of the liquid is given by

(A)

(B)

(C)

(D)

Solution: (D)

Cross-sectional area

Volume of liquid flowing per second

Mass of the liquid flowing out per second

Initial momentum of liquid per second

mass of liquid flowing Speed of liquid

Since the liquid does not rebound after impact, the momentum after impact is zero.

Rate of change of momentum

According to Newton’s second law, the force exerted on wall

rate of change of momentum

13. The and coordinates of a particle moving in a plane are given by ( ) ( ) and

( ) ( ) where, ( ) and are positive constants of appropriate dimensions and

is time. Then, which of the following is not true?

(A) The path of the particle is an ellipse

(B) Velocity and acceleration of the particle are perpendicular to each other at

(C) Acceleration of the particle is always directed towards a fixed point

(D) Distance travelled by the particle in time interval between and

is a

Solution: (D)

( ) ( )

, i.e. equation of ellipse

Now, ( ) ( )

( ) ( )

( ) ( )

at

perpendicular to

Also, , i.e. directed towards a fixed point

14. White light is used to illuminate two slits in Young’s double slit experiment. The separation

between the slits is and the screen is at a distance ( ) from the slits. At a point on the

screen directly in front of one of the slits, which wavelengths are missing?

(A)

(B)

(C)

(D)

Solution: (C)

The situation is shown in the figure

The path difference between the waves reaching the point is

( ) ⁄ .

/

⁄

0

1

For a dark band

( )

where, or

( )

Hence, the missing wavelengths are

,…….

15. A skier starts from rest at point and slides down the hill without turning or breaking. The

friction coefficient is . When he stops at point , his horizontal displacement is . What is the

height difference between and ?

(The velocity of the skier is small so that the additional pressure on the snow due to the

curvature can be neglected. Neglect also the friction of air and the dependence of on the

velocity of the skier.)

(A)

(B)

(C)

(D)

Solution: (A)

According to question, the situation is shown in the figure

For a sufficiently safe-horizontal displacement can be considered straight. If the

corresponding length of path element is , the friction force is given by

and the work

done by the friction force equals force times displacement

Adding up, we find that along the whole path the total work done by the friction force is .

By energy conservation this must equals the decrease in potential energy of skier.

Hence,

16. A bicycle wheel rolls without slipping on a horizontal floor. Which one of the following is

true about the motion of points on the rim of the wheel, relative to the axis at the wheel’s

centre?

(A) Points near the top move faster than points near the bottom

(B) Points near the bottom move faster than points near the top

(C) All points on the rim move with the same speed

(D) All points have the velocity vectors that are pointing in the radial direction towards the

centre of the wheel

Solution: (A)

We have, ⁄

Hence, velocity of point on rim increases with for and decreases with for

.

17. The planets with radii and , have densities respectively. Their atmospheric

pressures are and respectively. Therefore, the ratio of masses of their atmospheres,

neglecting variation of within the limits of atmosphere is

(A) ⁄

(B) ⁄

(C) ⁄

(D) ⁄

Solution: (D)

Acceleration due to gravity,

Atmospheric pressure can be given by

where, weight of atmosphere,

Surface area of the planet

( )

( )

18. A thin symmetrical double convex lens of refractive index is placed between a

medium of refractive index to the left and another medium of refractive index

to the right. Then, the system behaves as

(A) A convex lens

(B) A concave lens

(C) A glass plate

(D) A convexo concave lens

Solution: (C)

For first refracting surface,

For parallel beam of light;

For second refracting surface,

Hence, the combination behaves as glass plate.

19. A wide hose pipe is held horizontally by a fireman. It delivers water through a nozle at one

lirte per second. On increasing the pressure, this increases to two litres per second. The fireman

has now to

(A) Push forward twice as hard

(B) Push forward four times as hard

(C) Push backward four times as hard

(D) Push backward twice as hard

Solution: (B)

Rate of change of mass,

( )

Volume of liquid flowing per second

This is proportional to velocity

By doubling the volume of liquid flow per second, the force becomes four times. When liquid

flows forward, the hose pipe tends to come backward. So, to keep it intact, it should be pushed

forward. Thus, the hose pipe should be pushed forward four times.

20. The wavelength of a photon and the de-Broglie wavelength of an electron have the same

value. Find the ratio of energy of photon to the kinetic energy of electron in terms of mass ,

speed of light and planck constant.

(A)

(B)

(C)

(D)

Solution: (D)

The de-Broglie wavelength

…(i)

Energy of photon

(since is same) …(ii)

Energy of Photon

Kinetic energy of photon

⁄

Substituting value of from Equation (i), we get

(

)

21. A non-conducting ring of radius carries a total charge of distributed

non-uniformly on its circumference producing on its circumference on electric field ,

everywhere in space.

The value of the line integral ∫ ( )

( being centre of ring) in volts is

(A)

(B)

(C)

(D) Zero

Solution: (A)

From definition of potential difference ∫

potential difference at infinity and at

centre of ring

But by convention

∫ ( )

22. The upper half of an inclined plane of inclination is perfectly smooth while the lower half

rough. A block starting from rest at the top of the plane will again come to rest at the bottom if

the coefficient of friction between the block and the lower half of the plane is given by

(A)

(B)

(C) ( )⁄

(D) ⁄

Solution: (A)

Suppose length of plane is . When block descends the plane, rise in kinetic energy = fall in

potential energy

Work done by friction (reaction) distance

( ) ( ⁄ )

( ) ( ⁄ )

Now, work done = change in KE

( ) ( ⁄ )

⁄

23. Two masses and respectively are connected by a massless spring as shown in

figure. A force of acts on the mass. At the instant shown is figure the mass

has acceleration of ⁄ . The value of acceleration of mass is

(A) ⁄

(B) ⁄

(C) ⁄

(D) ⁄

Solution: (A)

Equation of motion of mass is

Force on -mass is to the right. As action and reaction ale equal and opposite, the

reactions force -on mass to the left.

Equation of motion of mass is

⁄

24. A cylinder rolls up an inclined plane, reaches some height and then rolls down (without

slipping throughout these motions). The directions of the frictional force acting on the cylinder

are

(A) Up the incline while ascending and down the incline while descending

(B) Up the incline while ascending as well as descending

(C) Down the incline while ascending and up the incline while descending

(D) Down the incline while ascending as well as descending

Solution: (B)

See given the figure.

It is obvious from figure, that during ascending, a retarding, i.e. anticlockwise moment is

required. It should be remembered that torque due to friction has the same sense the angular

acceleration.

25. A liquid is allowed into a tube of truncated cone shape. Identify the correct statement from

the following.

(A) The speed is high at the wider end and low at the narrow end

(B) The speed is low at the wider end and high at the narrow end

(C) The speed is same at both ends in a streamline flow

(D) The liquid flows with uniform velocity in the tube

Solution: (B)

For an incompressible liquid equation of continuity

constant or

Therefore, at the wider end speed below and at the narrow end speed will be high.

26. Two soap bubbles coalesce. It is noticed that, whilst joined together, the radii of the two

bubbles are and where . Then the radius of curvature of interface between the two

bubbles will be

(A)

(B)

(C) ( )⁄

(D) ( )⁄

Solution: (C)

According to given figure,

Let the radius of curvature of the common internal film surface of the double bubble formed by

two bubbles be . Excess of pressure as compared to atmosphere inside is ( ⁄ ). In double

bubble, the pressure difference between and on either side of the common surface

This will be equal to ( ⁄ )

or

(

)

or

27. The displacement of a particle along the -axis is given by . The motion of the

particle corresponds to

(A) Simple harmonic motion of frequency ⁄

(B) Simple harmonic motion of frequency ⁄

(C) Non simple harmonic motion

(D) Simple harmonic motion of frequency ⁄

Solution: (C)

Given,

or (

) [ ]

or

Now,

and ( ⁄ )

Here, is not directly proportional to ( ) which is a condition for SHM.

28. Mercury boils at . However, mercury thermometers are made such that they can

measure temperature upto . This is done by

(A) Maintaining vacuum aboves mercury column in the stem of the thermometer

(B) Filling nitrogen gas at high pressure above the mercury column

(C) Filling oxygen gas at high pressure above the mercury column

(D) Filling nitrogen gas at low pressure above the mercury column

Solution: (B)

If we fill nitrogen gas at high pressure above mercury level, the boiling point of mercury is

increased which can extend to the range upto ( ).

29. Two identical glass spheres filled with air are connected by a horizontal glass tube. The glass

tube contains a pellet of mercury at its mid-point. Air in one sphere is at and the other is at

. If both the vessels are heated through , then neglecting the expansions of the bulbs

and the tube

(A) The mercury pellet gets displaced towards the sphere at lower temperature

(B) The mercury pellet gets displaced towards the sphere at higher temperature

(C) The mercury pellet does not get displaced at all

(D) The temperature rise causes the pellet to expand without any displacement

Solution: (C)

Let and be the number of moles in the bulbs at and , respectively. Then,

…(i)

When the vessels are heated, let the volume of low temperature be and that of the other be

. Since, pressure are same, hence

and

…(ii)

From Equations (i) and (ii), we get

Thus, the mercury pellet remains at the same position.

30. A nucleus has mass represented by ( ). If and denote the mass of proton

and neutron respectively and the binding energy (in MeV) then,

(A) [ ( ) ( ) ]

(B) [ ( ) ( )]

(C) [ ( )]

(D) ( ) ( )

Solution: (B)

In the case of formation of nucleus the evolution of energy equals to the binding energy of the

nucleus takes place due to disappearance of a fraction of total mass. If the quantity of mass

disappearing is , then the binding energy is

From the above discussion, it is clear that the mass of the nucleus must be less than the sum of

the masses of the constituent neutrons and protons. We can then write

( )

Where ( ) is the mass of the atom of mass number atomic number . Hence, the

binding energy of nucleus is

[ ( )]

[ ( ) ( )]

31. A graph between pressure (along -axis) and absolute temperature, (along -axis) for

equal moles of two gases has been drawn. Given that volume of second gas is more than

volume of first gas. Which of the following statement is correct?

(A) Slope of gas 1 is less than gas 2

(B) Slope of gas 1 is more than gas 2

(C) Both have some slopes

(D) None of the above

Solution: (B)

According to ideal gas equation, or

represents slope of the graph

As the number of moles are the same for thee two gases,

(Given)

( ) ( )

or ( ) ( )

32. A piece of blue glass heated to a high temperature and a piece of red glass at room

temperature are taken inside a dimly-lit room. Then,

(A) The blue piece will look blue and the red piece will look red as usual

(B) The red piece will look brighter red and the blue piece will look ordinary blue

(C) The blue will look brighter as compared to the red piece

(D) Both the pieces will look equal red

Solution: (C)

When blue glass is heated at high temperature, it absorbs all the radiation of higher wavelength

except blue. If it is taken inside a dimly-lit room, it emits all the radiation of higher wavelength,

hence it looks brighter as compared to the red piece.

33. A certain charge is divided into two parts and . How the charge and must be

related so that when and ( ) is placed at a certain distance apart experience maximum

electrostatic repulsion?

(A)

(B)

(C)

(D)

Solution: (A)

The electrostatic force of repulsion between the charge and ( ) at separation is given

by

( )

If is maximum, then ⁄

i.e.

( )

As

is constant, therefore

or

34. A charged particle ‘ ’ is shot with speed towards another fixed charged particle . It

approaches upto a closest distance and then returns. If were given a speed , the

closest distance of approach would be

(A)

(B)

(C) ⁄

(D) ⁄

Solution: (D)

At closest distance its whole KE is converted into PE

In next case,

( )

(

) ⁄

35. A long block of mass is at rest on a smooth horizontal surface. A small block of mass

⁄ is placed on at one end and projected along with some velocity . The coefficient of

friction between the block is . Then, the accelerations of blocks and before reaching a

common velocity will be respectively

(A)

(towards right),

(towards left)

(B) (towards right), (towards left)

(C)

(towards right), (towards left)

(D) (towards right),

(towards left)

Solution: (C)

The force causing the motion of is frictional force between and ,

So, acceleration of

(

)

(towards right)

Block experiences frictions force toward left

towards left

36. A beam of light composed of red and green rays is incident obliquely at a point on the face

of a rectangular glass slab. When coming out on the opposite parallel face, the red and green

rays emerge from

(A) Two points propagating in two different non-parallel directions

(B) Two points propagating in two different parallel directions

(C) One point propagating in two different directions

(D) One point propagating in the same direction

Solution: (B)

We know that in any medium except vacuum or air, the velocities of different colours are

different. Therefore, both red and green colours are refracted at different angles of refraction.

So, after emerging from glass slab through opposite parallel faces, they appear at two different

points and move in two different parallel direction.

37. The plane face of a plano convex lens is silvered. If be the refractive index and , the

radius of curvature of curved surface, then system will behave like a concave mirror of

curvature

(A)

(B) ⁄

(C) ( )⁄

(D) [( ) ( )⁄ ]

Solution: (C)

When an object is placed in front of such a lens, the rays first of all refracted from the convex

surface, then refract from the polished plane surface and again refracts from convex surface. If

and be the focal lengths of lens (convex surface) and mirror (plane polished surface)

respectively, then effective focal length is given by

(

)

( ) (

)

( )

or

( ) or

( )

38. The maximum numbers of possible interference maxima for slit separation equal to twice

the wavelength in Young’s double slit experiment is

(A) Infinite

(B) Five

(C) Three

(D) Zero

Solution: (B)

The condition of interference maxima is

Given,

⁄

The magnitude of lies between 0 and 1

When

When ⁄

When

Thus, there is central maximum ( ), on other side of it maxima lie at

, so maximum number of possible interference maxima is 5.

39. An isotropic point source of light is suspended metre vertically above the centre of

circular table of radius metre. Then, the ratio of illumenances at the centre to that at the edge

of the table is

(A) (

)

(B) (

)

(C) ,

- ⁄

(D) ,

- ⁄

Solution: (C)

According to question, the situation is shown in the figure below

( )

…(i)

The illumination at the edge is given by

( )

( ) …(ii)

From figure,

√( )

( ) ⁄

Dividing Equation (i) by Equation (ii), we get

⁄

( ) ⁄⁄

( ) ⁄

.

/

⁄

.

/

⁄

40. In the given figure, what is the magnetic field induction at point .

(A)

(B)

(C)

(D)

Solution: (C)

Magnetic field due to straight wire above is zero

i.e. (since, )

the magnetic field due to semi circular part

(

)

( ⁄ )

The magnetic field due to lower straight portion

(upward)

Net magnetic field

(upwards)

41. - plots for two gases during adiabatic process as shown in figure plots 1 and 2 should

correspond respectively to

(A)

(B)

(C)

(D)

Solution: (B)

Slope of adiabatic process of - diagram

(

)

i.e. slope

From graph ( ) ( )

for monoatomic gas ( ) is greater than for diatomic gas ( )

42. The half-life period of a radioactive element is same as the mean life of anothe

radioactive element . Initially, both of the have the same numbers of atoms then,

(A) and have the same decay rate initially

(B) and decay at the same rate always

(C) will decay at a faster rate than

(D) will decay at a faster rate than

Solution: (C)

Half life of mean life of

Let be decay constants of , then condition (1) implies

As rate of decay ; hence decay of will be faster than that of .

43. A source emits electromagnetic waves of wavelength . One beam reaches the observer

directly and other after reflection from a water surface, travelling extra distance and with

intensity reduced to ⁄ as compared to intensity due to the direct beam alone. The resultant

intensity will be

(A) ( ⁄ ) fold

(B) ( ⁄ ) fold

(C) ( ⁄ ) fold

(D) ( ⁄ ) fold

Solution: (D)

We know that a phase change of occurs when the reflection takes place at the boundary of

denser medium. This is equivalent to a path difference of ⁄ .

Total phase difference

Thus, the two waves superimpose in phase.

Resultant amplitude √ √(

)

√

Resultant intensity (

√ )

fold.

44. The following circuit represents

(A) OR gate

(B) XOR gate

(C) AND gate

(D) NAND gate

Solution: (B)

Output of upper AND gate

Output of lower AND gate

Thus, output of OR gate

This is Boolean expression for XOR gate.

45. Two identical conducting balls and have positive charges and respectively. But

. The balls are brought together so that they touch each other and then kept in their

original positions. The force between them is

(A) Less than that before the balls touched

(B) Greater than that before the balls touched

(C) Same as that before the balls touched

(D) Zero

Solution: (B)

According to coulomb’s law, the force of repulsion between them is given by

When the charged spheres and are brought in contact, each sphere will attain equal charge

Now, the force of repulsion between them at the same distance is

(

) (

)

(

)

As (

)

46. A positively charged ball hangs from a silk thread. We put a positive test charge at a

point and measure ⁄ , then it can be predicted that the electric field strength

(A) ⁄

(B) ⁄

(C) ⁄

(D) Cannot be estimated

Solution: (A)

Due to presence of test charge in front of positively charged ball, there would be a

redistribution of charge on the ball. In the redistribution of charge, there will be less charge on

front half surface and more charge on the back half surface. As a result, the net force

between ball and charge will decrease, i.e. the electric field is decreased. Thus, actual electric

field will be greater than ⁄ .

47. Capacitor of capacitance and capacitor of capacitance are separately

charged fully by a common battery. The two capacitors are then separately allowed to

discharged through equal resistors at time

(A) The current in each of the two discharging circuits is zero at

(B) The currents in the two discharging circuits at are equal but non-zero

(C) The currents in the two discharging circuits at

(D) Capacitor loses 40% of its initial charge sooner than loses 40% of initial charge.

Solution: (B)

Here, and in the two circuits are same, hence the currents in the two discharging

circuits at ( ⁄ ) will be same.

We know that, time constant of a resistance and capacitance circuit is . Here, time constant

of first circuit (capacity ) is half of the time constant of second circuit (capacity

). Hence, loses 50% its initial charge sooner.

48. A uniform electric field and a uniform magnetic field acting along the same direction in a

certain region. If an election is projected along the direction of the fields with a certain velocity,

then

(A) It will turn towards left of direction of motion

(B) It will turn towards right of direction of motion

(C) Its velocity will increase

(D) Its velocity will decrease

Solution: (D)

The magnetic field will not apply any force on the electron. On the other hand, the electric field

will apply a force on the electron in opposite direction of the motion. As a result, the velocity of

the electron will decrease.

49. To reduce the range of voltmeter, its resistance need to be reduced. A voltmeter has

resistance and range . Which of the following resistances when connected in parallel will

convert it into a voltmeter of range ⁄ ?

(A)

(B) ( )

(C) ( )

(D) None of these

Solution: (D)

When a resistance is connected in parallel, it reduces the resistance of combination but the

range is not reduced. For the purpose of reducing the range the resistance in series with the

galvanometer need to be reduced.

This cannot be achieved by connecting a resistance in parallel with voltmeter. It should be

noted that the range of voltmeter can only be increased but cannot be decreased.

50. A uniform rod of length is free to rotate in a vertical plane about a fixed horizontal axis

through . The rod begins rotating from rest from its unstable equilibrium position. When, it

has turned through an angle , its angular velocity is given by

(A) √(

)

(B) √(

)

(C) √(

)

(D) √(

)

Solution: (A)

When the rod rotates through an angle , the centre of gravity falls through a distance . From

( ⁄ )

or

( )

Decrease in PE

( ) …(i)

The decrease in P.E. is equal to the kinetic energy of rotation (

)

( )

(

) …(ii)

From Equations (i) and (ii), we get

.

/

( )

√

51. A stick of length end mess lies on a frictionless horizontal surface on which it is free to

move in any way. A ball of mass moving with speed collides elastically with the stick as

shown in fig below. If after the collision, the ball comes to rest, then what should be the mass

of the ball?

(A)

(B)

(C) ⁄

(D) ⁄

Solution: (D)

Applying the law of conservation of momentum

…(i)

By conservation of angular momentum

( ⁄ ) (

) …(ii)

As the collision is elastic, we have

…(iii)

Substituting the values, we get

⁄

52. The mass of a proton is 1847 times that of an electron. A electron and a proton are injected

into a uniform electric field at right angle to the direction of the field with the same initial K.E.

(A) The electron trajectory will be less curved than the proton trajectory

(B) Both the trajectories will be straight

(C) The proton trajectory will be less curved than the electron trajectory

(D) Both the trajectories will be equally curved.

Solution: (D)

. In electric field,

The curvature of the trajectory is proportional to ⁄ . Since and are same for both

particles, hence the trajectories will have the same curvature.

53. Two condensers, one of capacity and the other of capacity

, are connected to a -volt

battery, as shown.

The work done in charging fully both the condensers is

(A)

(B)

(C)

(D)

Solution: (C)

The two condensers in the circuit are in parallel order, hence

The work done in charging the equivalent capacitor is stored in the form of potential energy

Hence,

(

)

54. A capacitor of capacitance is connected as shown in the figure. The internal resistance

of the cell is . The amount of charge on the capacitor plates is

(A)

(B)

(C)

(D)

Solution: (D)

In steady state, there will be no current in the capacitor branch. Net resistance of the circuit

Current drawn from the cell

Potential drop across two parallel branches

So, charge on the capacitor plates

55. A photo cell is illuminated by a small bright source placed away. When the same source

of light is placed away, the electrons emitted by photo cathode

(A) Carry one quarter of their previous energy

(B) Carry one quarter of their previous momenta

(C) Are half as numerous

(D) Are one quarter as numerous

Solution: (D)

(

)

when source is placed away, then ⁄ . The number of electrons emitted is directly

proportional to intensity. Hence, number of emitted electrons is reduced to one-fourth.

56. is right angled triangular plane of uniform thickness. The sides are such that

as shown in figure. are moments of inertia about and , respectively. Then

which of the following relations is correct?

(A)

(B)

(C)

(D)

Solution: (B)

The moment of inertia of a body about an axis depends not only on the mass of the body but

also on the distribution of mass about the axis. For a given body mass is same, so it will depend

only on the distribution of mass about the axis. The mass is farthest from axis , so is

maximum mass is nearest to axis , so is minimum.

Hence, the correct sequence will be

57. An ice-berg of density is floating in water of density . The

percentage of volume of ice-berg outside the water is

(A)

(B)

(C)

(D)

Solution: (C)

Let the volume of ice-berg is and its density is . If this ice-berg floats in water with volume

inside it then

(

)

(

)

(

)

58. The potential of an atom is given by ( ⁄ ) where is a constant and is the

radius of the orbit. Assuming Bohr’s model to be applicable, which variation of with is

possible ( being principal quantum number)?

(A)

(B) ⁄

(C)

(D) ⁄

Solution: (A)

Given that, ( ⁄ )

Field

(

)

(

) ⁄

( ) ⁄

Bohr’s quantum condition

or

59. The temperature of source and sink of a heat engine are and , respectively. An

inventor claims its efficiency to be 26%, then

(A) It is impossible

(B) It is possible with high probability

(C) It is possible with low probability

(D) Data are insufficient

Solution: (A)

Efficiency of hear engine is

Here,

Hence, efficiency is impossible for a given heat engine.

60. You are given resistance wire of length and a battery of negligible resistance. In

which of the following cases is largest amount of heat generated?

(A) When the wire is connected to the battery directly

(B) When the wire is divided into two parts and both the parts are connected to the battery in

parallel

(C) When the wire is divided into four parts and all the four parts are connected to the battery

in parallel

(D) When only half of the wire is connected to the battery

Solution: (C)

Let be the resistance of the wire

( )

( ) Resistance of each part will be ⁄ . When they are connected in parallel, the resistance will

be

⁄ .

Hence,

( ) In case of four wires connected in parallel, the resistance will be ⁄

( )

[ ⁄ ]

Hence, largest amount of heat will be generated in case of four parts connected in parallel.