Q 11-04-025JEE MainEAMCET 2010 (Engineering)Medium
A smooth block is released from rest on a $45°$ inclined plane and it slides a distance $d$. The time taken to slide is $n$ times that on a smooth inclined plane. The coefficient of friction is
Answer: (A) $\mu_k = 1 - \dfrac{1}{n^2}$
Concept. (Read as: on a rough $45°$ incline the time is $n$ times that on a smooth one.) Same distance: $a_s = n^2a_r$.
Step 1. Equation. $\sin45° = n^2(\sin45° - \mu_k\cos45°) \Rightarrow 1 = n^2(1 - \mu_k)$.
Step 2. Solve. $\mu_k = 1 - \dfrac{1}{n^2}$.
Answer. $\mu_k = 1 - \dfrac{1}{n^2}$ (Option A).
Solution by Sreeraj P, M.Sc Physics