Question

For a rigid body, if the velocity of its centre of mass is zero at all times, then: (1) Linear momentum of the body is (II) Net external force on the body must be zero (II) Kinetic energy of the body must be zero Which of the above statement(s) is (are) correct?

Answer 1

The correct statement is (II) Net external force on the body must be zero.

Step-by-step explanation:

In order for the velocity of the center of mass of a rigid body to be zero at all times, the net external force acting on the body must be zero.

This is due to the conservation of momentum principle, which states that when the net external force is zero, the total momentum of the system is conserved or constant. Therefore, if the linear momentum of the body is zero, it means that the net external force on the body must also be zero.

Regarding kinetic energy, it depends on the movement of the body. If the body’s centre of mass is at rest, it does not necessarily mean that the whole body is without motion. It could still rotate or have internal motion.

However, if we assume the body is not rotating or moving internally, then the kinetic energy would indeed be zero. Therefore, the true state of the kinetic energy depends on other factors besides the motion of the centre of mass