Laws of Motion

JEE Main level, single correct, medium

178 of 210

Question 178 of 210

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

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Answer: (B) 1−1n21-\frac{1}{n^2}

The coefficients of kinetic friction between the object and the incline
μ=tan⁡θ(1−1n2)\mu=\tan \theta\left(1-\frac{1}{\mathrm{n}^2}\right)
⇒μ=1−1n2(∵θ=45∘)\Rightarrow \mu=1-\frac{1}{\mathrm{n}^2} \quad\left(\because \theta=45^{\circ}\right)

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