There are two inclined surfaces of equal length $(L)$ and same angle of inclination $45^{\circ}$ wit

Question

There are two inclined surfaces of equal length $(L)$ and same angle of inclination $45^{\circ}$ 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

Professor PC Thomas Classes · Answer

(b) : Given : Angle of inclinatin, $	heta=45^{\circ}$ $t_{	ext {rough }}=2 t_{	ext {smooth }}$ Length of both inclined surfaces is equal. For smooth surface, initial velocity is zero, i.e., $u=0$, the distance ' $S$ ' is given by \ $ S=\frac{1}{2} a_{	ext {smooth }} t_{	ext {smooth }}^2 $ Acceleration of smooth plane is $a_{	ext {smooth }}=g \sin 	heta$ Using $	heta=45^{\circ}$, we get \