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

A small ball `B` of mass `m` is suspended with light inelastic string

1.	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, isA. `mg`B. `mg(2-costheta)`C. `mg(3-2costheta)`D. none of these
Answer» Correct Answer - D 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)`

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