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 $a_C$ respectively at any instant $t$. It is possible that
(i) $v_0=0,a_C=0$ (ii) $v_0\ne 0,a_C=0$; (iii) $v_0=0,a_C\ne 0$; (iv) $v_0\ne 0,a_C\ne 0$
Then

• A. (iii) and (iv) are true
• B. (i) and (ii) are true
• C. (i) and (iii) are true
• D. (i), (iii) and (iv) are true

Answer 1

The correct option is A (iii) and (iv) are true

Since a non-zero external force is acting on the system of particles,

therefore the acceleration of the center of mass of the system can never be zero.

Acceleration of center of mass is always given by $a=\frac{F}{M}$

where $F$ is the net external force and $M$ is the mass of the system.

Therefore , options (i) and (ii) are incorrect.

Now, the velocity of the center of mass can take zero as well as non-zero

values.

Hence options (iii) and (iv) are correct.