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 center 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.
Given: Length of the rod= L
Let the mass of the particle = m
Mass of the rod= M
Velocity at which it strikes the rod= v
Velocity of the rod after striking= V’
Consider it as a single system
No external torque is applied on the system
Using law of conservation of the linear momentum
Using law of conservation of the angular momentum
Therefore, distance travelled:
V’t= V’
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