A smooth tunnel is dug along the radius of the Earth that ends at the centre. A ball is released from the surface of Earth along the tunnel. If the coefficient of restitution for the collision between the ball and the surface of the tunnel is 0 . 2 then the distance travelled by the ball before the second collision at the centre is n R S . Find the value of n .

Question

A smooth tunnel is dug along the radius of the Earth that ends at the centre. A ball is released from the surface of Earth along the tunnel. If the coefficient of restitution for the collision between the ball and the surface of the tunnel is 0 . 2 then the distance travelled by the ball before the second collision at the centre is n R S . Find the value of n .,

MARKS App · Accepted Answer

a = - G M R 3 x a = - ω 2 x v c = ω A = G M R 3 × R After collision velocity of the ball towards A, v C = e v C = 0.2 G M R = 1 5 G M R Let now amplitude be A, then A ′ = v C ω = 1 5 G M R G M R 3 = R 5 Net distance = R + R 5 + R 5 = 7 R 5

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