When a block moves down a smooth inclined plane of inclination θ , its velocity on reaching the bottom is v . When it slides down a rough inclined plane of same inclination, its velocity on reaching the bottom is v / n , where n is a number greater than 1 . The coefficient of friction between the block and the rough surface is

Question

When a block moves down a smooth inclined plane of inclination θ , its velocity on reaching the bottom is v . When it slides down a rough inclined plane of same inclination, its velocity on reaching the bottom is v / n , where n is a number greater than 1 . The coefficient of friction between the block and the rough surface is, μ = 1 - 1 n 2 tan ⁡ θ, μ = 1 - 1 n 2 cot ⁡ θ, μ = 1 - 1 n 2 1 2 tan θ, μ = 1 - 1 n 2 1 2 cot θ

MARKS App · Accepted Answer

For smooth incline, v 2 = 2 g sin θ × s … … ( 1 ) For rough incline, v n 2 = 2 g sin θ - μ cos θ × s … … ( 2 ) On solving (1) and (2), we obtain, μ = 1 - 1 n 2 tan θ

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