A body takes n times as much time to slide down a 4 5 ∘ rough incline as it takes to slide down a smooth 4 5 ∘ incline. The coefficient of friction between the body and the incline will be

The coefficient of friction, Here, μ θ = tan θ ( 1 − n 2 1 ) = 4 5 ∘ ∴ μ = tan 4 5 ∘ ( 1 − n 2 1 ) = 1 − n 2 1

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PhysicsNLMFrictionMedium2 minPYQ_2012

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A body takes $n$ times as much time to slide down a $4 5^{\circ}$ rough incline as it takes to slide down a smooth $4 5^{\circ}$ incline. The coefficient of friction between the body and the incline will be

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Solution:

The coefficient of friction, Here, $μ θ = tan θ (1 - \frac{1}{n ^{2}}) = 4 5^{\circ}$ $∴$ $μ = tan 4 5^{\circ} (1 - \frac{1}{n ^{2}}) = 1 - \frac{1}{n ^{2}}$

Stream:MHT_CETSubject:PhysicsTopic:NLMSubtopic:Friction

⏱ 2mℹ️ Source: PYQ_2012

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