The time taken by an object to slide down 45 ° rough inclined plane is n times as it takes to slide down a perfectly smooth 45 ° incline plane. The coefficient of kinetic friction between the object and the incline plane is: (a) 1 - 1/n² (b) 1 + 1/n² (c) √(1 - 1/n²) (d) √((1)/(1-n²))

Answer: (a). At 45°: asmooth = g/√(2), arough = g/√(2)(1-μ). t ∝ 1/√(a) ⇒ n² = (1)/(1-μ) So the answer is (a) μ = 1 - 1/n².

The time taken by an object to slide down 45 ° rough inclined plane… | JEE Main 2023 (29 Jan, Shift 2)

Q15JEE Main 2023 · 29 JAN · SHIFT 2Medium

Friction on an Incline

The time taken by an object to slide down 45 ${}^\circ$ rough inclined plane is n times as it takes to slide down a perfectly smooth 45 ${}^\circ$ incline plane. The coefficient of kinetic friction between the object and the incline plane is:

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Answer: (a)

At $45^\circ$ : $a_{smooth} = \dfrac{g}{\sqrt{2}}$ , $a_{rough} = \dfrac{g}{\sqrt{2}}(1-\mu)$ .
$t \propto \dfrac{1}{\sqrt{a}} \Rightarrow n^2 = \dfrac{1}{1-\mu}$
So the answer is (a) $\mu = 1 - \dfrac{1}{n^2}$ .

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