System of Particles and Rotational Motion - Result Question 5

5. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2 v$ at any instant, then the speed of centre of mass of the system will be:

[2010]

(a) $2 v$

(b) zero

(c) 1.5

(d) $v$

Show Answer

Answer:

Correct Answer: 5. (b)

Solution:

  1. (b) If no external force action a system of particles, the centre of mass remains at rest. So, speed of centre of mass is zero.

Force acting on the rigid body,

$\vec{F}=M \vec{a} _{cm}=\frac{M d^{2} \vec{r}}{d t^{2}}$

When external force acting on the rigid body is zero.

$ \vec{F}=M \frac{d}{d t}( \vec{V} _{cm})=0 \Rightarrow \vec{V} _{cm}=\text{ Constant } $

So, when no external force acts on a body its centre of mass will remain at rest or move with constant velocity.