Question

A uniform rod of length L and mass 4m lies on a frictionless horizontal surface on which it is free to move anyway. A ball of mass m moving with speed v as shown in figure collides with the rod at one of the ends. If ball comes to rest immediately after collision with the rod then find out angular velocity $\omega$ of rod just after collision.

Answer 1

Let us choose the origin of the system at the centre of mass of the rod AB. Thus, Initial angular momentum $L_i=mvL/2$, since the rod is not moving. After collision, the particle comes to rest and hence final angular momentum is $L_f=\left(4m\right)\left(L^2/12\right)\omega$

Since no torques are acting on the system, angular momentum is conserved $mv\left(L/2\right)=4m\left(L^2/12\right)\omega .$ Solving, we get, $\omega =3V/2L$

The correct option is (b)