A bob of mass `m` is projected with a horizontal velocity `v=sqrt((gl)/(2))` as shown in figure. In consequence, it moves in a circular path in a vertical plane by the inextensible string which passes over the smooth fixed peg. Find the maximum angle that the bob swings in the left hand side.

Answer

`cos^-1(1/6)`

Explanation

Apply conservation of energy between A and B.
`1/2mv^2+mgl=(mg)(3l)/(2)[1-costheta]`
`v^2+2gl=3gl[1-cos theta]`
Put `v=sqrt((gl)/(2))`
`(gl)/(2)+2gl=3gl[1-costheta]`
`5/2=3[1-costheta]`
`implies5/6=1-costhetaimpliescostheta=1/6impliestheta=cos^-1(1/6)`