Question

If the net external forces acting on the system of particles is zero, then which of the following may vary?
(a) Momentum of the system
(b) Velocity of centre of mass
(c ) Position of centre of mass
(d) None of the above

Answer 1

Hint : Given that the net external forces acting on the system of particles is zero. And according to Newton’s second law the acceleration on the body is zero while at rest or in a uniform motion. Also when the acceleration is zero the velocity is a constant.

Complete step-by-step solution:
Given that the net external forces acting on the system of particles is zero. That is, the sum of all forces acting on the body is zero. There may be various forces acting on a body like the gravitational force, frictional force and forces due to electric field, gravitational field etc. Here the sum of various forces acting on the body is zero. Hence we can say that the acceleration acting on the body is zero according to Newton’s second law. Thus the velocity remains constant here. As the velocity is constant momentum also remains constant as it is the product of mass and velocity.
But for a system of particles the net force acting on it is zero. Then the acceleration on the body will be zero. The velocity of particles other than the centre of mass is not zero because of internal forces. But the velocity of the centre of mass is constant.
Initially the particle is at rest. Hence it requires some external force to start its motion. But if it is moving with uniform velocity and the net external force is zero. Then the acceleration acting on the body is zero. Hence it continues its motion with constant velocity. That means, it changes its position with varying time.
Therefore option (c ) is correct.

Note: According to Newton’s second law the force is equal to the rate of change of momentum. This shows that the body with greater mass has the larger momentum. For instance, a truck has larger momentum than a car.