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A board is moving with velocity v on a smooth horizontal plane. The upper surface of the board rough on which a ball falls with velocity v and rebounds with vertical 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 ball is

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$\frac{3}{5}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

answer is B.

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Detailed Solution

Impulse due to normal force on the ball

$N (dt) = m (v + \frac{v}{2}); Ndt = \frac{3 mv}{2}$
Impulse due to frictional force on plank

$μN (dt) = m (v - 0); μ (\frac{3 mv}{2}) = mv$

$\Rightarrow μ = \frac{2}{3}$

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