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Question

# A ball of mass ′m′ moving horizontally which velocity ′u′ hits a wedge of mass ′M′. the wedge is situated on a smooth horizontal surface. If after striking wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane. Calculate the coefficient of restitution e.

A

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B

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C

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D

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Solution

## The correct option is C As no external force are acting on the system in horizontal direction the linear momentum should be constant conserved in horizontal direction. Let velocity of wedge after collision be V. Then mu = MV ⇒ V = muM. . . . . . (i) As there is no impulse on the ball in the direction parallel to sloping side hence the velocity of ball along the slope (tangent direction) should remain unchanged. ⇒ucosθ = v sin θ which gives v = u cot θ . . . . . . (ii) The coefficient of restitution is given as (v2−v1)normal = e(u1−u2)normal [V sin θ−(−v cosθ)] = e[u sin θ−0] e = v sinθ+vcosθusinθ e = Vu+vucot θ = mM+(cot θ)cot θ (from(i)&(ii)) e = mM+cot2θ

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