Two bars of masses `m_1` and `m_2` connected by a weightless spring of stiffness `k`, rest on a smooth horizontal plane. Bar `2` is shifted by a small distance `x_0` to the left and released. The veloicyt of the centre of mass of the system when bar 1 breaks off the wall is

Options

A. (a) `x_0sqrt((km_2)/(m_1+m_2))`
B. (b) `(x_0)/(m_1+m_2)sqrt(km_2)`
C. (c) `x_0k(m_1+m_2)/(m_2)`
D. (d) `x_0(sqrt(km_1))/((m_1+m_2))`

Answer

B

Explanation

`1/2kx_0^2=1/2m_2v_2^2`
`:. v_2=sqrt((k)/(m_2))x_0`
`v_(CM)=(m_1v_1+m_2v_2)/(m_1+m_2)`
`=((sqrt(km_2))/(m_1+m_2))x_0` (as `v_1=0`)