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Question

A body of mass m is suspended from a string of length R. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete the vertical circle?


Solution

 

The tendency of the string to become slack is maximum when the particle is at the topmost point of the circle.
At the top, tension is given by T=mv2tRmg,where vt= speed of the particle at the top.
mv2tR=T+mg
For vt to be minimum, T=0vt=gR
If vb be the critical velocity of the particle at the bottom, then from conservation of energy
mg(2R)+12mv2t=0+12mv2b
Thus, vb=5gR
 
 

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