A smooth block is released at rest on a 45^ incline and then slides a distance d . The time taken to slide is n times as much to slide on a rough incl - Physics MCQ AIEEE 2026 | ExamTest.live

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A smooth block is released at rest on a 4 5^{\circ} incline and then slides a distance d . The time taken to slide is n times as much to slide on a rough incline than on a smooth incline. The coefficient of friction is:

Solution & Step-by-step Explanation

For a smooth incline: a_{1} = g sin θ .Time taken t_{1} = \frac{2 d}{g s i n θ} .For a rough incline: a_{2} = g (sin θ - μ_{k} cos θ) .Time taken t_{2} = \frac{2 d}{g ( s i n θ - μ _{k} c o s θ )} .Given t_{2} = n t_{1}, so t_{2}^{2} = n^{2} t_{1}^{2} : \frac{2 d}{g ( sin θ - μ _{k} cos θ )} = n^{2} \frac{2 d}{g sin θ} sin θ = n^{2} (sin θ - μ_{k} cos θ) For θ = 4 5^{\circ}, sin 4 5^{\circ} = cos 4 5^{\circ} = \frac{1}{2} : \frac{1}{2} = n^{2} (\frac{1}{2} - μ_{k} \frac{1}{2}) 1 = n^{2} (1 - μ_{k}) 1 - μ_{k} = \frac{1}{n ^{2}} ⟹ μ_{k} = 1 - \frac{1}{n ^{2}}

Try it yourself before checking the explanation above.

A smooth block is released at rest on a 4 5^{\circ} incline and then slides a distance d . The time taken to slide is n times as much to slide on a rough incline than on a smooth incline. The coefficient of friction is:

μ_{k} = 1 - \frac{1}{n ^{2}}

μ_{k} = 1 - \frac{1}{n ^{2}}

μ_{s} = 1 - \frac{1}{n ^{2}}

μ_{s} = 1 - \frac{1}{n ^{2}}

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