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

Explanation

`tan theta = v^(2)/(rg)`
`v= sqrt(rg tan theta)`. But `r=l sin theta`
`=sqrt(l sin theta g tan theta) = sqrt(l xx sin 10 xx 9.8 xx tan 10)`
`=sqrt(0.1736 xx 9.8 xx 0.1763) = 0.55` m/s
Period of revolution
`r= 2pi sqrt(g/h) = 2pi sqrt((l cos theta)/g) = 2 xx 3.14 xx sqrt((l xx cos 10)/(9.8)) = 1.9 s`