Question

A wagon of mass M can move without friction along horizontal rails. A simple pendulum consisting of a sphere of mass m is suspended from the ceiling of the wagon by a string of length L. At the initial moment the wagon and the pendulum are at rest and the string is deflected through an angle $\alpha$ from the vertical. Find the velocity of the wagon when the pendulum passes through its mean position.

Answer 1

When pendulum is deflected by 60 degree,height raised be

$h^{{}^{\prime }}=lcos{60}^o=\frac{1}{2}$

Change in height=$l-\frac{l}{2}=\frac{l}{2}$

Change in P.E=$\frac{mgl}{2}$

$\frac{1}{2}(m+M)V^2=\frac{mgl}{2}$

Since $mv=MV$

$V=\frac{m}{M}V$=$\frac{m}{M}\sqrt{\frac{10ml}{m+M}}$