A solid sphere has linear velocity v 0 = 4 m/s and angular velocity ω 0 = 9 rad/s as shown. Ground on which it is moving, is smooth. It collides elastically with a rough wall of coefficient of frictio

Question

A solid sphere has linear velocity v 0 = 4 m/s and angular velocity ω 0 = 9 rad/s as shown. Ground on which it is moving, is smooth. It collides elastically with a rough wall of coefficient of friction μ . Radius of the sphere is 1 m and mass is 2 kg. If the sphere after colliding with the wall rolls without slipping in opposite direction, then coefficient of friction μ is

TestHub · Accepted Answer

ω = ν R = 4 1 = 4 rad/s Let N be perpendicular force between wall and sphere at the time of collision and Δ t the time of impact, then N Δ t = Δ P = 8 m ( as Δ ν = 8 m/s ) ..... (1) Further R μ N Δ t = Δ I ω = 2 5 mR 2 5 ..... (2) As Δ ω = 5 rad/s Dividing Eq. (2) by Eq. (1), we get μ = 1 4

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