Rotational Motion Question 13
Question: Consider a two particle system with particles having masses $ m _1 $ and $ m _2 $ . If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?
[AIEEE 2006]
Options:
A) $ \frac{m _2}{m _1}d $
B) $ \frac{m _1}{m _1+m _2}d $
C) $ \frac{m _1}{m _2}d $
D) $ d $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] To keep the centre of mass at the same position, velocity of centre of mass is zero, so $ \frac{m _1{{{\vec{v}}}_1}+m _2{{{\vec{v}}}_2}}{m _1+m _2}=0 $ (where, $ {{\vec{v}}_1} $ and $ {{\vec{v}}_2} $ are velocities of particles 1 and 2 respectively)
$ \Rightarrow $ (and represent the small change in displacement so that andof particles)
Let 2nd particle has been displaced by distance then
Negative sign shows that both the particles have to move in opposite directions.
So,is the distance moved by 2nd particle to keep position of centre of mass unchanged.
