Consider a two particle system with particles having masses `m_(1)andm_(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?

Options

A. d
B. `(m_(2))/(m_(1))d`
C. `(m_(1))/(m_(1)+m_(2))d`
D. `(m_(1))/(m_(2))d`

Answer

D

Explanation

Suppose a particle of mass `m_(2)` moved a distance x toward centre of mass is x.
`therefore (m_(1)d+m_(2)(-x))/(m_(1)+m_(2))=r_(cm)`
`therefore m_(1)d-m_(2)x=0 [because r_(cm)=0]`
`therefore m_(1)d=m_(2)x`
`therefore x=(m_(1))/(m_(2))d`