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) $v$
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Answer:
Correct Answer: 5. (b)
Solution:
- (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.
