Question

A non-zero external force acts on a system of particles. The velocity and acceleration of the centre of mass are found to be $v_{0}$ and $a_{0}$ at an instant $t$ . It is possible that

• A. $v_{0}=0,a_{0}=0$
• B. $v_{0}=0,a_{0}\neq 0$
• C. $v_{0}\neq 0,a_{0}=0$
• D. $v_{0}≠0,a_{0}=1$

Answer 1

Answer: (B)

If the external force is non-zero then the acceleration of the centre of mass must be non-zero $\left(a_{0} = \frac{F_{e x t}}{M} \neq 0\right)$ . However, at a particular instant of time velocity of the centre of mass may be zero or non-zero. Hence $v_{0}=0,a_{0}\neq 0$
From the equation of velocity is in +ve direction and acceleration is in -ve direction, then at some moment velocity will become 0.