Laws Of Motion

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 \({1 \over {\sqrt x }}\left( {{{{\alpha ^2} - 1} \over {{\alpha ^2}}}} \right)\) where x = __________.