Question

A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be v₀ and a₀ at instant t. It is possible that
(a) v₀ = 0, a₀ = 0
(b) v₀ = 0, a₀ ≠ 0
(c) v₀ ≠ 0, a₀ = 0
(d) v₀ ≠ 0, a₀ ≠ 0

Answer 1

 (b) v₀ = 0, a₀ ≠ 0
 (d) v₀ ≠ 0, a₀ ≠ 0

If a non-zero external force acts on a system of particles, it causes the centre of mass of the system to accelerate with acceleration a₀ at any instant t. In such a case, the velocity of centre of mass of the system of particles is either v₀ or zero.