JEE Main 2021 — Laws Of Motion Question with Solution

When a body slides down from rest along a smooth inclined plane making an angle of 30$${}^{\circ }$$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha$$T, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $$\frac{1}{\sqrt{x}}\left(\frac{{\alpha }^2-1}{{\alpha }^2}\right)$$ where x = __________.