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 = $\underline{\hspace{2cm}}$.