Let a uniform circular disc of mass **m** and radius **R** is free to rotate in **Horizontal** Plane about a Point "O" at the **edge** ( Hinge at the Point "O" ) . A Man Having Same Mass **m** is standing at the point "A" which is just opposite diametric end point with respect to point "O" .

Now at time t=0 , man Starts moving with Constant velocity "${ u }_{ rel }$" with respect to disc.

Then Find The **angular displacement** of the **disc** (${ \theta }_{ disc }$ ) in the time interval when Man reaches again at point "A" at the disc.

If Your answer is ${ \theta }_{ disc }$ and it is expressed as :

$\\ { \theta }_{ disc }\quad =\quad \pi \quad -\quad \pi \quad \times \sqrt { \cfrac { a }{ b } }$.

Then Compute " a + b " ?

**Details**

$\bullet$ 'a' and 'b' are co-prime positive integers.

$\bullet$ Man moves on circumference of disc only.