Question

A small disc and a thin uniform rod of length L, whose mass is η times greater than the mas of disc, lie on a smooth horizontal plane.The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity v, after which it elastically collides with the end of the rod. Find the velocity of the disc angular velocity of the rod after the collision.At what value of h will the velocity of the disc after the collision be equal to zero ?Reverse the direction ?

Answer 1

The situation is shown in figure. If mass of disc is m, then mass of rod hm. if v1 and v2 be the velocities of the disc and rod after collision, using linear momentum conservation, we have

mv = mv1 + hmv2

or v = v1 + ηv2 ....(x)

If after collision, rod starts rotating with angular speed w, using consrvation of angular momentum we have

As collision is elastic, using kinetic energy conservation, we get

Solving for v1, we get

Here we can see that v1 is zero if h = 4 and v1 will be negative when η > 4.