Question

A uniform rod of length L lies on a smooth horizontal table. A particle moving on the table strikes the rod perpendicularly at an end and stops. Find the distance travelled by the centre of the rod by the time it turns through a right angle. Show that if the mass of the rod is four times that of the particle, the collision is elastic.

Answer 1

Let the mass of the particle = m & the mass of the rod = M
Let the particle strikes the rod with a velocity V.
If we take the two body to be a system,
Therefore the net external torque & net external force = 0
Therefore Applying laws of conservation of linear momentum
MV' = mV (V' = velocity of the rod after striking)
 V' / V = m / M
Again applying laws of conservation of angular momentum