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…

There are two inclined surfaces of equal length $\displaystyle (L)$ and same angle of inclination $\displaystyle 45^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes $\displaystyle 2$ times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ( $\displaystyle \mu_k$ ) between the object and the rough surface is close to