Q 11-04-004NEETNEET 2025Top questionMedium
There are two inclined surfaces of equal length ($L$) and same angle of inclination $45°$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes $2$ times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ($\mu_k$) between the object and the rough surface is close to
Answer: (D) $0.75$
Concept. Same distance from rest: $t \propto \dfrac{1}{\sqrt a}$.
Step 1. Accelerations. $t_r = 2t_s \Rightarrow a_r = \dfrac{a_s}{4}$.
Step 2. Solve. $g(\sin45° - \mu_k\cos45°) = \dfrac{g\sin45°}{4} \Rightarrow 1 - \mu_k = \dfrac14 \Rightarrow \mu_k = 0.75$.
Answer. $0.75$ (Option D).
Solution by Sreeraj P, M.Sc Physics