A given object takes n times more time to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is: (a) (1)/(2-n²) (b) 1 - 1/n² (c) √(1 - 1/n²) (d) √((1)/(1-n²))

Answer: (b). Reading "n times more time" as tr = n ts. At 45°: (tr)/(ts) = √(a₀/a) = (1)/(√(1-μ)) = n So the answer is (b) μ = 1 - 1/n².

A given object takes n times more time to slide down a 45° rough… | JEE Main 2018 (15 Apr, Shift 1)

Q24JEE Main 2018 · 15 APR · SHIFT 1Medium

Friction on an Incline

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

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Answer: (b)

Reading "n times more time" as $t_r = n\,t_s$ .
At $45^\circ$ : $\dfrac{t_r}{t_s} = \sqrt{\dfrac{a_0}{a}} = \dfrac{1}{\sqrt{1-\mu}} = n$
So the answer is (b) $\mu = 1 - \dfrac{1}{n^2}$ .

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