When a body slides down from rest along a smooth inclined plane making an angle of \( 30^\circ \) with the horizontal, it take 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 \(\dfrac{1}{\sqrt{x}}(\dfrac{a^2-1}{a^2}) \) where \(x=\)___________.
