A solid sphere has linear velocity V₀=4m/s and angular velocity ω₀=9rad/s as shown. Ground on which it is moving is smooth. It collides (e=1) with rough wall of coefficient of friction μ. Radius of sphere is 1m and mass 2kg.

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If the sphere rolls without slipping after collision, angular velocity after collision is 4 rad/s clock wise

If the sphere rolls without slipping after collision, μ=0.25

If the sphere rolls without slipping after collision, μ=0.5

If the sphere rolls without slipping after collision, angular velocity after collision is 4 rad/s anti clock wise

answer is A, B.

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Detailed Solution

$\begin{array}{l} NΔt = 2 {mV}_{0} \dots \dots . . (1) \\ - f R Δt = I (ω_{f} - ω_{i}) \dots \dots . . (2) \\ \Rightarrow - μ (NΔt) R = \frac{2}{5} {mR}^{2} (4 - 9) \Rightarrow μ = \frac{1}{4} \end{array}$

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