A uniform rod lies at rest on a frictionless horizontal surface. A particle, having a mass equal to that of the rod, moves on the surface perpendicular to the rod collides with it, and finally sticks to it. The minimum loss of KE in the collision , under the given conditions, is

Options

A. `5%`
B. `10%`
C. `20%`
D. `30%`

Answer

C

Explanation

The maximum loss occurs when the collision is "head-on" and the minimum is when it collides at a an end. Assume that the particle strikes the rod (of length `2 L` ) perpendicularly at a distance x from its centre. Apply conservation of momentum and angular momentum to calculate the final velocity of the rod and also its angular velocity. The fractional loss in `KE = 1//[3(x//L)^(2) + 2]`