Question

A rod of length $R$ and mass $M$ is free to rotate about a horizontal axis passing through hinge $P$ as in figure. First it is taken aside such that it becomes horizontal and then released. At the lowest point the rod hits the small block $B$ of mass $m$ and stops. Find the ratio of masses such that the block $B$ completes the circular track of radius $R$. Neglect any friction.

Answer 1

By using concept of center of mass ,center of mass of rod is at C at R/2 from ends.

K energy of rod at lowest point before hitting of block $=Mg\frac{R}{2}$..(1)

Energy required to complete the circulat truck by the block m is $=\frac{1}{2}m\left(5gR\right)$..(2)

Equating (1) and (2),

$Mg\frac{R}{2}=\frac{1}{2}m\left(5gR\right)$

$\frac{M}{m}=5$