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) $0.75$
Starting from rest, $L = \dfrac{1}{2}at^2$, so $t \propto \dfrac{1}{\sqrt{a}}$.
$t_{\text{rough}} = 2t_{\text{smooth}}$ means $a_{\text{rough}} = \dfrac{a_{\text{smooth}}}{4}$:
$$g(\sin 45° - \mu_k\cos 45°) = \frac{g\sin 45°}{4}$$
Since $\sin 45° = \cos 45°$:
$$1 - \mu_k = \frac{1}{4} \;\Rightarrow\; \mu_k = 0.75$$
Solution by Sreeraj P, M.Sc Physics