A simple pendulum of length `L` having a bob of mass `m` is first taken aside so that the string forms the tight angle with the verticle and then released. The string hits a peg which is fixed at a distance below the point of suspension and the bob starts going in a circle centered at the peg. find the minimum value of `y` for which the bob goes in a complete circle about the peg.

Explanation

When the string becomes verticle, the speed of bob
`v^(2)=u^(2)+2gL=2gLimpliesv=sqrt(2gL)`
To complete the verticle center about new point `O_(1)`,
`vgesqrt(5g(L-y))`
`sqrt(2gLgesqrt(5g(L-y))`
`2L.=(5L-5y)implies5yge3L`
`yge(3L)/(5)`
`y_(min)=(3L)/(5)=0.6L`