Q 11-04-102JEE MainJEE Main 2023 (29 Jan, Shift 2)Medium
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
Answer: (D) $1-\dfrac{1}{n^2}$
For the same length, $s=\tfrac12at^2$ gives $t\propto\dfrac{1}{\sqrt a}$, so $\dfrac{a_{smooth}}{a_{rough}}=n^2$.
$$\frac{g\sin45^\circ}{g\sin45^\circ-\mu g\cos45^\circ}=n^2\ \Rightarrow\ \frac{1}{1-\mu}=n^2\ \Rightarrow\ \mu=1-\frac{1}{n^2}$$
Solution by Sreeraj P, M.Sc Physics