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.

Tension in string when it is vertical, is

Options

A. `mg`
B. `mg(2-costheta)`
C. `mg(3-2costheta)`
D. none of these

Answer

D

Explanation

Loss in `PE =` gain in `KE`
`mg(L-Lcostheta)=1/2mv_(1)^(2)+1/2mv_(2)^(2)`
Applying momentum conservation principle in horizontal direction.
`P_(ix)=P_(fx)`
`0=mv_(1)-mv_(2)`
`:. v_(1)=v_(2)=v`
`:. Mg(L-Lcostheta)=mv^(2)`
`:. v=sqrt(gl(1-costheta))`
`=T-mg=(m(2v^(2)))/l`
` :. T=mg+(4mgl(1-costheta))/l`
`:. T=mg+4mg(1-costheta)`