A massless Rod of Length 'L' with small Stone of mass ' m ' at the end is Hinged at point 'O' as shown in the figure and occupies a strictly Vertical Position, touching a body of mass M . A Light Gentle jerk sets the system in motion. For what mass ratio M/m will the rod form an angle $\alpha$ with the horizontal at the moment of the separation from the body ? Friction should be neglected everywhere. if it can be expressed as $\displaystyle{\cfrac { M }{ m } =\cfrac { a-b\sin { \alpha } }{ \sin ^{ c }{ \alpha } } }$

Then Find a + b + c

**Assumptions**

$\bullet$ Here assume That $\displaystyle{\alpha \quad \in \quad (o,\cfrac { \pi }{ 2 } )}$

**Source**: $\text{Asked in my test}$