<p>When a body slides down from rest along a smooth inclined plane making an angle of <span class="equation">\(30^0\)</span>&nbsp;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&nbsp;<span class="equation">\(\alpha\)</span>T, where&nbsp;&nbsp;is a constant greater than 1. The co-efficient of friction between the body and the rough plane is&nbsp;<span class="equation">\(\frac{1}{\sqrt{x}}\)</span>&nbsp;<span class="equation">\(\begin{pmatrix}
\frac{\alpha^2-1}{\alpha}
\end{pmatrix}\)</span>&nbsp;where x = ______​​​​​​​​​​​​​​</p>