In a two-particle system with particle masses `m_1 and m_2`, the first particle is pushed towards the centre of mass through a distance `d`, the distance through which second particle must be moved to keep the centre of mass at the same position is

Options

A. `(m_(2) d)/( m_1)`
B. d
C. `(m_1 d)/( (m_1 + m_2) )`
D. `(m_1 d)/( m_2)`

Answer

D

Explanation

In given condition,
`m_1 (x-d_1 ) = m_2 (y-d_2)`
`m_1 x - m_1 d_1 = m_2 y- m_2 d_2`
`m_1 d_1 = m_2 d_2`
`d_2 = (m_1)/(m_2) d_1 " "(because "constants")`
`d_(2) = (m_1)/(m_2) d " "(because d_1 = d)`