A classical mechanics problem by Miraj Shah

Consider a body, attached to a string of length rr, to be initially at rest in the vertical plane. It can be proved that if we give the body an initial velocity of v>5grv>\sqrt{5gr}, then, the body can make complete revolutions in the vertical plane about the point of suspension.

Let us consider that the body, initially at rest, is given a velocity v<5grv<\sqrt{5gr}. If at this value of vv the body eventually hits the point of suspension then we can write:

v2=(a+b)gr  . v^2 = (a+\sqrt{b})gr \; .

Find a×ba\times b.

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