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 $\frac { 1 } { \sqrt { x } } \frac { \alpha ^ { 2 } - 1 } { \alpha ^ { 2 } }$ where $x =$ $\_\_\_\_$.
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 $\frac { 1 } { \sqrt { x } } \frac { \alpha ^ { 2 } - 1 } { \alpha ^ { 2 } }$ where $x =$ $\_\_\_\_$.