System Of Particles And Rotational Motion Ques 52
52. 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: 52.(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.
BETA
