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Questions:

Multiple Choice Question

55 x 1 = 55

An object of mass 10 kg is hanging on a spring scale which is attached to the roof of a lift. If the lift is in free fall, the reading in the spring scale is

(a)

98 N

(b)

zero

(c)

49 N

(d)

9.8 N

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then

(a)

K_A > K_B >K_C

(b)

K_B < K_A < K_C

(c)

K_A < K_B < K_C

(d)

K_B > K_A > K_C

If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be

(a)

64.5

(b)

1032

(c)

182.5

(d)

730

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

(a)

\({r_2\over r_1}\)

(b)

\(({r_2\over r_1})^2\)

(c)

\({r_1\over r_2}\)

(d)

\(({r_1\over r_2})^2\)

The linear momentum and position vector of the planet is perpendicular to each other at

(a)

perihelion and aphelion

(b)

at all points

(c)

only at perihelion

(d)

no point

For a particle, revolving in a circle with speed, the acceleration of the particle is ______________.

(a)

along the tangent

(b)

along the radius

(c)

along its circumference

(d)

zero

In non-uniform circular motion, the resultant acceleration makes an angle with the radius vector is ___________.

(a)

\(\tan^{-1}(\frac{ra_t}{V^2})\)

(b)

\(\tan_{-1}(\frac{a_t}{(\frac{r}{v^2})})\)

(c)

\(\tan^{-1}(\frac{rv^2}{at})\)

(d)

\(\tan^{-1}(\frac{r+at^2}{v^2})\)

The angle of inclined plane with the horizontal such that an object placed on it begins to slide is ___________.

(a)

angle of friction

(b)

angle of repose

(c)

angle of response

(d)

angle of retardation

In a gravitational field, the work done in moving a body from one point into another depends on _____________.

(a)

initial and final positions

(b)

distance between them

(c)

actual distance covered

(d)

velocity of motion

10.

For elastic collision, coefficient of restitution is ____________.

(a)

(b)

(c)

0 < e < 1

(d)

\(\infty \)

11.

A bomb at rest explodes. The total momentum of all its fragments is _____________.

(a)

zero

(b)

infinity

(c)

always 1

(d)

always greater then 1

12.

If a force F is applied on a body and the body moves with velocity v, the power will be ______________.

(a)

F.V

(b)

F/V

(c)

FV²

(d)

F/V²

13.

In a vernier caliper, n divisions of vernier scale coincides with (n - 1) divisions of main scale. The least count of the instrument is ______________

(a)

\(\frac{1}{n}\)MSD

(b)

\({n\over n+1}\)MSD

(c)

\({ n+1\over n}\)MSD

(d)

\({ n+1\over n-1}\)MSD

14.

The dimensional formula for heat capacity__________________

(a)

[ML²T²]

(b)

[M L² K^-1]

(c)

[M L² T² K^-1]

(d)

[M L² T² K^-1]

15.

The shift in the position of an object when viewed with two eyes, keeping one eye closed at a time is known as___________.

(a)

basis

(b)

fundamental

(c)

parallax

(d)

pendulum

16.

If a car and a scooter have the same momentum, then which one is having greater speed?

(a)

scooter

(b)

car

(c)

both have same velocity

(d)

data insufficient

17.

The moment of inertia of a body about a given axis is 1.2 kgm². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration 25 radian/sec² must be applied about that axis lor a duration of ____________.

(a)

4 s

(b)

2 s

(c)

8 s

(d)

10 s

18.

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is ______________.

(a)

33.3km/h

(b)

20\(\sqrt{2}\) km/h

(c)

25\(\sqrt{2}\)km/h

(d)

35km/h

19.

A bus travelling the first one-third distance at a speed of 10 km/h, the next one-third at 20 km/h and at last one-third at 60 km/h. The average speed of the bus is _____________.

(a)

9km/h

(b)

16km/h

(c)

18km/h

(d)

48km/h

20.

If r and k represent the radius and radius of gyration of a rolling body, the ratio of the rotational kinetic energy to the total kinetic energy of the body is _____________.

(a)

k²:r²

(b)

(k² + r²) : r²

(c)

r²:(k²+r²)

(d)

k²:(k²+r²)

21.

The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is ________________.

(a)

24 N s

(b)

20 N s

(c)

12 N s

(d)

6 N s

22.

While measuring acceleration due to gravity, by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error , of 3% in the value of time period. The percentage error in the measurement of 'g' is _______________.

(a)

(b)

(c)

10%

(d)

23.

The dimension of torque is _____________.

(a)

ML²T²

(b)

M²L²T²

(c)

ML²T^-1

(d)

MLT^-2

24.

Which one of the following is not a conservative force?

(a)

Gravitational force

(b)

Electrostatic force between two changes

(c)

Magnetic force, between two magnetic dipoles

(d)

Frictional force

25.

What is the resultant vectors, when 2 vectors are at right angles to each other?

(a)

\(R=\sqrt{P^2+Q^2}\)

(b)

R = P + Q

(c)

R = P - Q

(d)

\(R=\sqrt \frac{P}{Q}\)

26.

First law of Newton deals with the ______________.

(a)

concept of inertia alone

(b)

definition of force alone

(c)

either (a) or (b)

(d)

concept of inertia and definition of force

27.

The value of one Angstrom is _______________.

(a)

10¹⁰m

(b)

10^-10m

(c)

10^-8m

(d)

10^-15m

28.

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

29.

When a body is moving on a surface, the force of friction is called_____ friction.

(a)

Static

(b)

Kinetic

(c)

Limiting

(d)

Rolling

30.

A body whose momentum is constant must have constant _______________.

(a)

Force

(b)

Acceleration

(c)

Velocity

(d)

All

31.

A machine gun has mass 15 kg. It fires 15 g bullet at the rate of 200 bullets per minutes with a speed of 150 m/s. Then the recoil velocity of the gun is ____________.

(a)

20 ms^-1

(b)

15 ms^-1

(c)

150 ms^-1

(d)

0.2 ms^-1

32.

An iron sphere of mass 8 kg has the same diameter as a copper sphere of mass 4 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same ____________.

(a)

acceleration

(b)

momenta

(c)

Potential Energy

(d)

Kinetic Energy

33.

If I, \(\alpha \) and \(\tau \) are MI, angular acceleration and torque respectively of a body rotating about any axis with angular velocity \(\omega \), then _____________.

(a)

\(\tau =I\omega \)

(b)

\(\tau =I\alpha \)

(c)

\(\alpha =r\omega \)

(d)

\(\alpha =r\omega \)

34.

A couple produces____ motion.

(a)

linear and rotational

(b)

purely rotational

(c)

purely linear

(d)

35.

The mass of an iron sheet is 0.250 kg and volume of the sheet is 1.5m³ Then what is the density of the iron sheet? Express the result in SI unit system.

(a)

0.267 kg m^-3

(b)

0.167 kg m^-3

(c)

0.255 kg m^-3

(d)

0.285 kg m^-3

36.

The speed of an object v = 90km/h. The same quantity of speed in m/s is ______________.

(a)

(b)

(c)

(d)

180

37.

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

38.

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

39.

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

(d)

40.

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

41.

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

(a)

the center point of the circle

(b)

the point on the circumference of the circle

(c)

any point inside the circle

(d)

any point outside the circle

42.

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

(b)

L/2

(c)

(d)

L/\(\sqrt{2}\)

43.

A body of mass 1 kg is thrown upwards with a velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?(Take g = 10 ms^-2)

(a)

20 J

(b)

30 J

(c)

40 J

(d)

10 J

44.

A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

(a)

\(\sqrt2:1\)

(b)

\(1:\sqrt2\)

(c)

2:1

(d)

1:2

45.

A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

46.

If force |F|, velocity |V| and time |T| are taken as to fundamental units then the dimensions of mass are _______________.

(a)

FV^-1T

(b)

FV^-1T

(c)

FVT^-1

(d)

FVT^-2

47.

If a person moving from pole to equator, the centrifugal force acting on him

(a)

increases

(b)

decreases

(c)

remains the same

(d)

increases and then decreases

48.

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure.The minimum value of the force F is

(a)

Less than mg

(b)

Equal to mg

(c)

Greater than mg

(d)

Cannot determine

49.

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R₆_0°

(b)

R_30° = 4R₆_0°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R₆_0°

50.

If a particle executes uniform circular motion in the xy plane in clockwise direction, then the angular velocity is in

(a)

+y direction

(b)

+z direction

(c)

-z direction

(d)

-x direction

51.

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms^-2)

(a)

77.3 m

(b)

78.4 m

(c)

80.5 m

(d)

79.2 m

52.

Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is

(a)

\(\sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(b)

\(\sqrt { \frac { { { m }_{ 1 }h }_{ 1 } }{ { { m }_{ 2 }h }_{ 2 } } } \)

(c)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \sqrt { \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \)

(d)

\(\frac { { m }_{ 1 } }{ { m }_{ 2 } } \)

53.

Which one of the following Cartesian coordinate systems is not followed in physics?

(a)

(b)

(c)

(d)

54.

The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

(a)

[L]

(b)

[LT^-1]

(c)

[LT^-2]

(d)

[LT^-3]

55.

If \(\pi=3.14,\) then the value of \({\pi}^{2}\) is

(a)

9.8596

(b)

9.860

(c)

9.86

(d)

9.9

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Answers Key:

Multiple Choice Question

55 x 1 = 55

(b)
zero

(a)
K_A > K_B >K_C

T² = C (R + h)³
\(\therefore T \alpha (R_E)^\frac{3}{2}\)
R_E = 2R_E
\(\therefore T \alpha (2R_E)^\frac{3}{2}\)
Time period increases by \(2^\frac{2}{3}\)= 2\(\sqrt 2\)
No. of days in a year = (365.4) \(\times\)2\(\sqrt 2\)
= 1032

(a)
\({r_2\over r_1}\)

(a)
perihelion and aphelion

(b)
along the radius

(a)
\(\tan^{-1}(\frac{ra_t}{V^2})\)

(b)
angle of repose

10.

(b)
1

11.

(a)
zero

12.

(a)
F.V

13.

(a)
\(\frac{1}{n}\)MSD

14.

(d)
[M L² T² K^-1]

15.

16.

(a)
scooter

17.

(b)
2 s

18.

19.

20.

(d)
k²:(k²+r²)

21.

22.

(d)
7%

23.

(b)
M²L²T²

24.

(d)
Frictional force

25.

(a)
\(R=\sqrt{P^2+Q^2}\)

26.

(d)
concept of inertia and definition of force

27.

(b)
10^-10m

28.

Mass per unit length = m
Velocity = v
(mass of water pumped in one second)
M = mv
\(\text { Kinetic energy }=\frac{1}{2} M v^{2}\)
\(=\frac{1}{2} m v^{3}\)

29.

(b)
Kinetic

30.

31.

(d)
0.2 ms^-1

32.

(a)
acceleration

33.

(b)
\(\tau =I\alpha \)

34.

(b)
purely rotational

35.

(b)
0.167 kg m^-3

36.

(b)
25

37.

Acceleration of the solid sphere while rolling down without slipping
\(a_{1}=\frac{g \sin \theta}{1+\frac{k^{2}}{r^{2}}}\)
Acceleration developed while slipping down \(a_{2}=g \sin \theta\)
\(\text { Required ratio } \frac{a_{1}}{a_{2}}=\frac{g \sin \theta}{1+\frac{k^{2}}{r^{2}}} / g \sin \theta\)
\(\frac{a_{1}}{a_{2}}=\frac{1}{1+\frac{k^{2}}{r^{2}}}\)
\(\text { For a solid sphere } \frac{k^{2}}{r^{2}}=\frac{2}{5}\)
\(\therefore \text { Ratio of accelerations } \frac{a_{1}}{a_{2}}=\frac{1}{1+\frac{2}{5}}\)
\(=\frac{1}{5+\frac{2}{5}}=\frac{1}{\frac{7}{5}}=\frac{5}{7}\)
\(\therefore a_{1}: a_{2}=5: 7 \)

38.

The moments of inertia of two discs are I_a and I_b respectively The angular velocity of the disc A is \(\omega\).
The sum of kinetic energies of two discs before coming in contact is \(k_{1}=\frac{1}{2} I_{a} \omega_{1}^{2}+\frac{1}{2} I_{b} \omega_{2}^{2}\)
\(\text { But angular velocity of the disc be is } \omega_{2}=0 \ \text {(rest)}\)
\(\therefore k_{1}=\frac{1}{2} I_{a} \omega_{1}^{2}\)
The final kinetic energy of the two discs system \(k_{2}=\frac{1}{2} \frac{I_{a}^{2} \omega_{1}^{2}}{I_{a}+I_{b}}\)
The loss of kinetic energy is
\(k_{1}-k_{2} =\frac{1}{2} I_{a} \omega^{2}-\frac{1}{2}\left[\frac{I a^{2} \omega_{1}^{2}}{I_{a}+I_{2 b}}\right] \)
\(=\frac{1}{2} \frac{\left[I_{1}\left(I_{a}+I_{b}\right) \omega^{2}-I_{a}^{2} \omega^{2}\right]}{I_{a}+I_{b}} \)
\(k_{1}-k_{2} =\frac{1}{2} \frac{I_{a} b}{\left(I_{a}+I_{b}\right)} \omega^{2} \)

39.

For any spring kl = constant
Length of the longer piece
\(=\frac{2 l}{3} \)
\(\therefore k^{1} \times \frac{2 l}{3} =k l \)
\(\therefore k^{1}=\frac{k l \times 3}{2 l}=\frac{3}{2} k \)
\(\therefore k^{1}=\frac{3}{2} k \)

40.

\(\text { Kinetic energy } E_{k}=\frac{p^{2}}{2 m}\)
\(\frac{\Delta E_{k}}{E_{k}}=\frac{2 \Delta p}{p}\)
\(\text {Given that } \frac{\Delta p}{p}=0.1\)
∴ Increase in kinetic energy
\(\frac{\Delta E_{k}}{E_{k}}=2 \frac{\Delta p}{p} \)
\(\frac{\Delta E_{k}}{E_{k}}=2 \times 0.1=0.2 \% \)

41.

(a)
the center point of the circle

42.

\(K \cdot E=\frac{1}{2} I \omega^{2} ; \quad L=I \omega ; \quad K \cdot E=\frac{2^{2}}{2^{2}} \)
\(\therefore K \cdot E \alpha L^{2} \quad E_{1} \alpha L_{1}^{2} \quad E_{2} \alpha L_{2}^{2}\)
\(\frac{E_{1}}{E_{2}}=\left(\frac{L_{1}}{L_{2}}\right)^{2} \)
\(\text { Here } E_{1}=E \quad E_{2}=\frac{E}{2} \)
\(L_{1}=L \quad \quad L_{2}=? \)
\(\frac{E}{\frac{E}{2}}=\left(\frac{L}{L_{2}}\right)^{2} \)
\(\frac{2 E}{E}=\left(\frac{L}{L_{2}}\right)^{2}\left(\frac{L_{1}}{L_{2}}\right)^{2}=2 \)
\(\therefore \frac{L}{L_{2}}=\sqrt{2} \)
\(L_{2}=\frac{L}{\sqrt{2}} \)

43.

Mass = 1kg
Velocity v = 20m/s
Height h = 18 m
\(g=10 \mathrm{~m} / \mathrm{s}^{2}\)
\(\text { Potential energy } P . E=m g h\)
\(=1 \times 10 \times 18 =180 \mathrm{~J} \)
\(\text { Kinetic energy } K . E=\frac{1}{2} m v^{2}\)
\(K . E=\frac{1}{2} \times 1(20)^{2}\)
\(=\frac{1}{2} \times 20 \times 20=200 J\)
\(\text { Loss of energy due to air friction }= K.E - P.E\)
\(=200-180=20 \mathrm{~J}\)

44.

\(m_{1} =1, \quad m_{2}=2 \)
\(K . E . =m g(h-x) \)
\(\text { For both balls }(h-x)\)
\(=40 \text { i.e.) Same }\)
\(g=\text { constant }\)
\(\therefore K \cdot E_{1}=m_{1} g(h-x)=m_{1} g \times 40 \)
\(K \cdot E_{2}=m_{2} g(h-x)=m_{2} g \times 40 \)
\(\therefore \frac{K \cdot E_{1}}{K \cdot E_{2}}=\frac{m_{1} g \times 40}{m_{2} g \times 40}=\frac{m_{1}}{m_{2}} \)
\( \therefore K \cdot E_{1}: K \cdot E_{2}=1: 2 \)

45.

(a)
pure rotation

46.

47.

(a)
increases

48.

49.

Range is same for the angle if projection \(\theta \text { and } 90-\theta\)

50.

Use thumb rule

51.

(b)
78.4 m

52.

For freely falling body, velocity while the body, hit the ground \(v=\sqrt{2 g h}\)
\(v_{1}=\sqrt{2 g h_{1}} \text { and } v_{2}=\sqrt{2 g h_{2}} \)
\(\therefore \frac{m_{1} v_{1}}{m_{2} v_{2}}=\frac{m_{1} \sqrt{h_{1}}}{m_{2} \sqrt{h_{2}}}=\frac{m_{1}}{m_{2}} \sqrt{\frac{h_{1}}{h_{2}}}\)

53.

Answers (a), (b) and (c) are all anticlockwiseand answer (d) alone is in the clockwise direction

54.

\(v=a t+b t^{2}\)
\(\text { Dimensional equation is } \mathrm{LT}^{-1}\)
\(=a T=b T^{2}\)
\(\therefore \text { The dimension of } b=\frac{\mathrm{LT}^{-1}}{\mathrm{~T}^{2}}=\mathrm{LT}^{-3}\)

55.

\(\pi=3.14 \)
\(\pi^{2} =3.14 \times 3.14 \)
\(=9.8596=9.86 \)