Two beads `A` and `B` of masses `m_(1)` and `m_(2)` respectively, are threaded on a smooth circular wire of radius a fixed in a vertical plane. `B` is stationary at the lowest point when `A` is gently dislodged from rest at the highest point. A collided with `B` at the lowest point. The impulse given to `B` due to collision is just great enough to carry it to the level of the centre of the circle while `A` is immediately brought to rest by the impact.
What is the coefficient of restituting between the beads?

Options

A. `1`
B. `1/2`
C. `1/3`
D. `1/sqrt(2)`

Answer

D

Explanation

`e=(v_(2)-v_(1))/(u_(1)-u_(2))=(sqrt(2ga)-0)/(2sqrt(ga)-0)=1/sqrt2`