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 is moved, so as to keep the center of mass at the same position?

Options

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

Answer

C

Explanation

Initially,
`0=(m_(1)(-x_(1))+m_(2)x_(2))/(m_(1)+m_(2))impliesm_(1)x_(1)=m_(2)x_(2)" "...(1)`
Finally,
The centre of mass is at the origin

`therefore 0=(m_(1)(d-x_(1))+m_(2)(x_(2)-d.))/(m_(1)+m_(2))`
`implies0=m_(1)d-m_(1)x_(1)+m_(2)x_(2)-m_(2)d.impliesd.=(m_(1))/(m_(2))d["from "(1).]`