A board is moving with velocity `v` on a smoother horizontal plane. The upper surface of the board is rough on which a ball falls with velocity `v` and rebounds with velocity `(v)/(2)`. The mass of the board is same as that of ball. After the collision, the board comes to state of rest. The co-efficient of friction between the board and the ball is

Options

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

Answer

B

Explanation

Impluse due to normal force on the ball
`N(dt) = m(v+(v)/(2)) , N dt = (3mv)/(2)`
impluse due to frictional force on plank
`mu N (dt) = m(v-0), mu((3mv)/(2)) = mv , mu = (2)/(3)`