A solid sphere of radius r is gently placed on a rough horizontal surface with an initial angular speed ω 0 but no linear velocity. If the coefficient of friction is μ , then the time t when the slipping will stop is

Question

A solid sphere of radius r is gently placed on a rough horizontal surface with an initial angular speed ω 0 but no linear velocity. If the coefficient of friction is μ , then the time t when the slipping will stop is, 2 7 r ω 0 μ g, 3 7 r ω 0 μ g, 4 7 r ω 0 μ g, r ω 0 μ g

MARKS App · Accepted Answer

Let m be the mass of the sphere. Since, it is a case of backward slipping, force of friction is in forward direction. Limiting friction will act in this case. Linear acceleration a = f m = μ mg m = μ g Angular retardation α = τ I = f · r 2 5 mr 2 = 5 2 μ g r Slipping will be stopped when v = rω at = r ( ω 0 - αt ) μ gt = r ( ω 0 - 5 2 μ g t r ) 7 2 μ gt = r ω 0 ∴ t = 2 7 r ω 0 μ g

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