In head - on collision between two particles `A` and `B` of same mass , `A` is moving with momentum `15 kg m//s` , `B` is stationary . During the impact , `B` gives impulse `10 N -s` to `A` . The coefficient of restitution is

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(1)/(4)`
D. `(1)/(5)`

Answer

B

Explanation

`mu + 0 = mv_(1) + mv_(2)`
`rArr v_(1) + v_(2) = u`
`v_(1) - v_(2) = -e( u - 0)`
`rArr v_(1) - v_(2) = -e u`
Solving the above equations , we get
`v_(2) = ((1 + e)u)/(2)`
`mv_(2) = ((1 + e) mu)/(2)`
Impulse `J = mv_(2) rArr 10 = ((1 + e)(15))/(2)`
`e = (1)/(3)`