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.

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