Two same masses are tied with equal lengths of strings and are suspended at the same point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This is given initial velocity u in vertical downward direction. It strikes the freely suspended mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is:
Text Solution
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As collision is elastic, freely suspended mass moves acquiring velocity of colliding mass after the collision. Also acquired velocity must be equal to 
to complete the circular motion.
Hence, mgL = 
mu 2 = 
m(5gl)
u = 
.
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