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JEE • PHYSICS • SYSTEM OF PARTICLES

System of particles practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Easy

1 of 26

Application +4 | -1

The angular velocity of a particle is given by

\omega = {t^4} + 2{t^3}

then its angular acceleration of the particle at

t = 1\,sec

\left( {rad\,{s^{ - 2}}} \right)

View answer and explanation

Correct option: C

Option C (10) is correct because the angular acceleration is the derivative of the angular velocity with respect to time, and evaluating the derivative at t=1 sec gives 10 rad/s².

2 Easy

2 of 26

Remembering +4 | -1

Centre of mass for a uniform semi-circular ring will be at (from centre)

View answer and explanation

Correct option: A

\frac{{2R}}{\pi }

Option A (

\frac{{2R}}{\pi }

) is correct because the center of mass of a uniform semi-circular ring is located at a distance of

\frac{{2R}}{\pi }

from the center of the ring.

3 Easy

3 of 26

Application +4 | -1

The angular speed of fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in

\mathrm{rad/}{\mathrm{s}^2}

is:

View answer and explanation

Correct option: C

4\,\pi

Option C (

4\pi

) is correct because it is calculated using the formula for angular acceleration, converting rpm to rad/s.

4 Easy

4 of 26

Application +4 | -1

If an angular momentum of a body of fixed M.I. increases by

50 \%

, its kinetic energy of rotation increases by:

View answer and explanation

Correct option: D

125 \%

Option D is correct because the angular speed is determined by conservation of angular momentum.

5 Easy

5 of 26

Application +4 | -1

Consider a system of two identical particles in which first one is accelerating with

2 {~m} / {s}^2

and second one is at rest. The centre of mass of this system will have an acceleration

View answer and explanation

Correct option: B

1 {~m} / {s}^2

Option B (

1 {~m} / {s}^2

) is correct because the acceleration of the center of mass is the average of the individual accelerations.

6 Easy

6 of 26

Remembering +4 | -1

1^{\circ}

is equal to

View answer and explanation

Correct option: D

Both (1) and (2)

Option D (Both (1) and (2)) is correct because

1^{\circ}

is equal to both

\frac{\pi}{180}

rad and 60'.

7 Easy

7 of 26

Application +4 | -1

A thick straight wire of length

4\pi \,m\,

is fixed at its midpoint and the bent in the form of a circle. The shift in its centre of mass is

View answer and explanation

Correct option: C

2 m

Option C (2 m) is correct because the shift in the center of mass is equal to the radius of the circle formed by bending the wire.

8 Easy

8 of 26

Analyzing +4 | -1

A solid sphere and hollow sphere of same mass and radius rotate about their diameter with same rotational kinetic energy. If torques of equal magnitude are applied on them, ratio of their angular displacement before they are bought to rest.

View answer and explanation

Correct option: A

0.042361111

Option A (01:01) is correct because if the torques applied are of equal magnitude and the initial rotational kinetic energies are the same, the angular displacements will be equal.

9 Easy

9 of 26

Application +4 | -1

Three masses are placed on the x – axis, 200 g at origin, 400 g at x = 20 cm and 600 g at x = 60 cm. The distance of the centre of mass from the origin is

View answer and explanation

Correct option: D

\frac{{110}}{3}\,cm

Option D (

\frac{{110}}{3}\,cm

) is correct because it is calculated using the center of mass formula for a system of particles.

10 Easy

10 of 26

Application +4 | -1

R

is the radius of gyration of a body of mass

M

and radius

r

, then the ratio of its rotational to translational kinetic energy in the rolling condition is

View answer and explanation

Correct option: B

\frac{R^2}{r^2}

Option B (

\frac{R^2}{r^2}

) is correct because the ratio of rotational to translational kinetic energy depends on the ratio of the square of the radius of gyration to the square of the radius.

11 Easy

11 of 26

Application +4 | -1

Moment of inertia of a ring of mass

m = 4\,gm

and radius

r = 1\,cm\,

about an axis passing through its edge and parallel to its natural axis is

View answer and explanation

Correct option: A

8\,g - c{m^2}

Option A (

8\,g - cm^2

) is correct because it is calculated using the parallel axis theorem for the moment of inertia of a ring.

12 Easy

12 of 26

Application +4 | -1

A train is moving with a speed of

12 \mathrm{~m} / \mathrm{s}

on rails which are

1.5 \mathrm{~m}

apart. To negotiate a curve of radius

400 \mathrm{~m},

the height by which the outer rail should be raised with respect to the inner rail is

\text{(Given } g=10 \mathrm{~m} / \mathrm{s}^2)

View answer and explanation

Correct option: D

5.4 \mathrm{~cm}

Option D (5.4 cm) is correct because it is calculated using the banking angle formula relating velocity, radius, and the distance between the rails.

13 Easy

13 of 26

Application +4 | -1

Two particles whose masses are

10 \mathrm{~kg}

and

30 \mathrm{~kg}

and their position vectors are

\hat{i}+\hat{j}+\hat{k}

and

-\hat{i}-\hat{j}-\hat{k}

respectively would have the centre of mass at

View answer and explanation

Correct option: A

-\frac{(\hat{i}+\hat{j}+\hat{k})}{2}

Option A (

-\frac{(\hat{i}+\hat{j}+\hat{k})}{2}

) is correct because it is the calculated center of mass position vector of the two particles.

14 Easy

14 of 26

Application +4 | -1

A shaft rotating at 6000 rpm is transmitting a power of

2\pi

kilowatt. Then magnitude of the driving torque is

View answer and explanation

Correct option: A

10 Nm

Option A (10 Nm) is correct because the driving torque is calculated using the formula

\tau = \frac{P}{\omega}

15 Easy

15 of 26

Application +4 | -1

Radius of gyration of a thin rod of mass 1 kg about an axis perpendicular to its length and passing through its centre is

\sqrt 3 \,m

. Then length of the rod is

View answer and explanation

Correct option: B

6 m

Option B (

20^{\circ} \mathrm{C}

) is correct because it is the temperature at which the pendulum clock neither gains nor loses time.

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16 Easy

16 of 26

Understanding +4 | -1

What are the coordinates of centre of mass of a point mass of

2 {~kg}

with coordinates

(2,3)

View answer and explanation

Correct option: D

(2,3)

Option D is correct because the center of mass of a single point mass is simply the location of that point mass.

17 Easy

17 of 26

Analyzing +4 | -1

When a sphere rolls down an inclined plane, then identity the correct statement related to the work done by friction force

View answer and explanation

Correct option: C

The net work done by friction is zero

Option C (The net work done by friction is zero) is correct because for pure rolling, the point of contact is instantaneously at rest, so friction does no work.

18 Easy

18 of 26

Application +4 | -1

Two rigid bodies A and B rotate with rotational kinetic energies

{E_A}\,and\,{E_B}

respectively. The moments of inertia of A and B about the axis of rotation are

{I_A}\,and\,{I_B}

respectively. If

{I_A} = {I_B}/4\,and\,{E_A} = 100\;{E_B}

the ratio of angular momentum

\left( {{L_A}} \right)

of A to the angular momentum

\left( {{L_B}} \right)

of B is

View answer and explanation

Correct option: C

Option C (5) is correct because the ratio of angular momentum is calculated using the relationship between rotational kinetic energy, moment of inertia, and angular momentum.

19 Easy

19 of 26

Application +4 | -1

The angular velocity of a particle is given by

\omega = {t^4} + 2{t^3}

then its angular acceleration of the particle at

t = 1\,sec

\left( {rad\,{s^{ - 2}}} \right)

View answer and explanation

Correct option: C

Option C (10) is correct because the angular acceleration is the derivative of the angular velocity with respect to time, and evaluating the derivative at t=1 sec gives 10 rad/s².

20 Easy

20 of 26

Analyzing +4 | -1

Statement I: Total torque on a system is independent of
the origin if the total external force is zero.
Statement II: Torque due to a couple is independent of
the origin.

View answer and explanation

Correct option: A

Statement I is true, Statement II is true; Statement II is
the correct explanation for Statement I

Option A is correct. If the net external force is zero, the total torque is independent of the origin, and the torque due to a couple is always independent of the origin, explaining the first statement.

21 Easy

21 of 26

Analyzing +4 | -1

A man standing on a platform holds weights in his outstretched arms. The system is rotated about a central vertical axis. If the man now pulls the weights inwards close to his body, then

View answer and explanation

Correct option: D

All of the above

Option D (All of the above) is correct because when the man pulls the weights inwards, his moment of inertia decreases, leading to an increase in angular velocity and kinetic energy while conserving angular momentum.

22 Easy

22 of 26

Analyzing +4 | -1

When a body is projected at an angle with the horizontal in the uniform gravitational field of the earth, the angular momentum of the body about the point of projection, as it proceeds along the path

View answer and explanation

Correct option: B

Increases continuously

Option B (Increases continuously) is correct because the torque due to gravity about the point of projection increases continuously as the perpendicular distance from the line of action of gravity to the point of projection increases.

23 Easy

23 of 26

Analyzing +4 | -1

For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the body

View answer and explanation

Correct option: D

Four rods forming a square of side

2 R

Option D (Four rods forming a square of side 2R) is correct because for the same total mass, distributing the mass farthest from the axis of rotation maximizes the moment of inertia.

24 Easy

24 of 26

Application +4 | -1

If all of a sudden the radius of the earth decreases, then

View answer and explanation

Correct option: B

The angular speed of the earth will increase

The angular speed of the earth will increase because, according to the conservation of angular momentum, if the radius decreases, the angular speed must increase to keep the angular momentum constant.

25 Easy

25 of 26

Application +4 | -1

A solid sphere of mass

m

rolls down an inclined plane a height

h

. Find rotational kinetic energy of the sphere.

View answer and explanation

Correct option: A

\frac{2}{7} m g h

Option A (

\frac{2}{7} m g h

) is correct because the rotational kinetic energy is a fraction of the total potential energy converted, and for a solid sphere, the fraction is 2/7.

26 Easy

26 of 26

Understanding +4 | -1

The centre of mass of system of particles does not depend on

View answer and explanation

Correct option: D

Force acting on the particle

Option D (Force acting on the particle) is correct because the center of mass depends only on the masses and positions of the particles, not the forces acting on them.

Revision notes and key takeaways

Review SYSTEM OF PARTICLES in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 26 single-correct-answer MCQs on SYSTEM OF PARTICLES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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