Motion of systems of particles and rigid body MCQ for NEET

A rigid body is defined as the body that has particles which are at a fixed distance from each other and remains constant. For any regular body, the centre of mass lies at the geometrical centre. Also, the turning motion in the rigid body is produced by the net torque.

The motion of systems of particles and rigid body has concepts such as the centre of mass, torque, angular momentum, conservation of angular momentum, the radius of gyration, and theorems related to perpendicular and parallel axes.

1. What is the radius of gyration of a uniform rod whose length is L and passes through the centre of mass

(a) $\frac{L}{\sqrt{3}}$

(b) $\frac{L}{\sqrt{2}}$

(c) $\frac{L}{2\sqrt{3}}$

(d) $\frac{L^{2}}{12}$

Answer: (c) $\frac{L}{2\sqrt{3}}$

2. By what percentage does the kinetic energy increase, if the linear momentum is increased by 50%

(a) 25%

(b) 50%

(c) 100%

(d) 125%

3. What is the angular momentum vector in an orbital motion?

(a) The vector is perpendicular to the orbital plane

(b) The vector is along the radius vector

(c) The vector is parallel to the linear momentum

(d) The vector is in the orbital plane

Answer: (a) The vector is perpendicular to the orbital plane

4. What is the acceleration of the rolling sphere at the centre of the plane with inclination, Ө to the horizontal?

(a) Zero

(b) Less than g sin Ө

(c) Greater than g sin Ө

(d) g sin Ө

Answer: (b) Less than g sin Ө

5. On which of the following factor does the moment of inertia of an object not depend upon

(a) Axis of rotation

(b) Angular velocity

(c) Distribution of mass

(d) Mass of an object

Answer: (b) Angular velocity

6. What is the frictional force of a round object with mass M and radius R which rolls down the inclined plane without slipping along the way

(a) There is a decrease in the rotational motion

(b) There is a decrease in the rotational and translational motion

(c) There is a conversion of translational motion into rotational motion

(d) Kinetic energy is converted into heat

Answer: (c) There is a conversion of translational motion into rotational motion

7. When the torque acting on the system is zero, which of the following is constant?

(a) Linear impulse

(b) Linear momentum

(c) Force

(d) Angular momentum

Answer: (d) Angular momentum

8. The angular momentum of a rigid body is L and its kinetic energy is halved. What happens to its angular momentum?

(a) L

(b) 2L

(c) $\frac{L}{2}$

(d) $\frac{L}{4}$

Answer: (c) $\frac{L}{4}$

9. Consider two objects a disk and a sphere that has the same radius but different masses which roll down the two inclined planes with the same altitude and length. Out of the two objects, which one gets to the bottom of the plane first?

(a) It is dependent on the masses of the objects

(b) Disk

(c) Sphere

(d) Both reach at the same time

10. What does $\frac{L^{2}}{2I}$ represent?

(a) Power

(b) The torque of a particle

(c) The potential energy of a particle

(d) The rotational kinetic energy of a particle

Answer: (d) The rotational kinetic energy of a particle

11. The motion of planets in the solar system is an example of conservation of

(a) Energy

(b) Linear momentum

(c) Angular momentum

(d) Mass

Answer: (c) Angular momentum

12. When does the moment of inertia of a body come into the picture?

(a) When the motion is rotational

(b) When the motion is linear

(c) When the motion is along a curved path

(d) None of the above

Answer: (a) When the motion is rotational

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