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) $\dfrac{5}{9}$
Concept. As before, $t\propto1/\sqrt a$ for the same length. "50% more" means $t_r=1.5\,t_s$.
Step 1. Ratio. $\dfrac{a_s}{a_r}=1.5^2=\dfrac94$.
Step 2. At $45^\circ$. $1-\mu=\dfrac49\Rightarrow\mu=\dfrac59$. (General rule at $45^\circ$: $t_r=nt_s$ gives $\mu=1-\dfrac1{n^2}$.)
Answer. $\dfrac59$ (Option C).
Solution by Sreeraj P, M.Sc Physics
