Q 11-04-058JEE MainJEE Main 2026 (4 Apr, Shift 1)Medium
The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^\circ$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ______
Answer: (C) $\dfrac{5}{9}$
For the same distance from rest, $t \propto \dfrac{1}{\sqrt{a}}$. $t_r = 1.5t_s$ means $a_s = 2.25a_r$:
$$g\sin 45^\circ = 2.25\,g(\sin 45^\circ - \mu\cos 45^\circ) \;\Rightarrow\; 1 - \mu = \frac{4}{9} \;\Rightarrow\; \mu = \frac{5}{9}$$
Solution by Sreeraj P, M.Sc Physics