A small ball `B` of mass `m` is suspended with light inelastic string of length `L` from a block `A` of same mass in which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle `theta` from equilibrium position and then released.
The displacement of centre of mass of `A + B` system till the string becomes vertical is

Options

A. zero
B. `L(1-costheta)`
C. `L/2(1-costheta)`
D. none of these

Answer

C

Explanation

`y_(cm)=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))`
`:. /_\y_(cm)=(m_(1)/_\y_(1)+m_(2)/_\y_(2))/(m_(1)+m_(2))`
`/_\y_(cm)=(0-mL(1-costheta))/(m+m)`
`:. /_\y_(cm)=L/2(1-costheta)` in downward direction.