An inclined plane is placed on a horizontal smooth surface. The plane is struck by an elastic ball whose velocity is horizontal just before the impact. The ball bounces off the inclined plane and then lands on it again at the point of first impact. Find the ratio of the masses of the ball and the inclined plane. (Angle $θ = 30^{\circ}$ )

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Detailed Solution

Conservation of linear momentum in horizontal direction
$m_{1} V_{1} = (m_{1} + m_{2}) V_{2}$
Coefficient of restitution = 1
$V_{y} \cos θ = V_{1} \sin θ$
Component of velocity of ball along the inclined plane remain same
$V_{1} \cos θ = V_{2} \cos θ + V_{y} \sin θ$
Solving
$\frac{m_{1}}{m_{2}} = \cot^{2} θ - 1$

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