# Use sum of product of vectors T and V

A small ring of mass $$m$$ can slide on a friction less rod. It is connected to a block of mass $$M$$. The rod is at a distance $$d$$ from the pulley. Initially the ring is at a distance $$d$$ from point $$O$$. Find the velocity of the block when the ring is at a distance $$d/2$$ from point $$O$$.

The answer is in form

$${ V }^{ 2 }=\frac { Mgd(a\sqrt { a } -\sqrt { b } ) }{ M+bm }$$

Find $$a+b$$.

×