A particle rests on the top of a smooth hemisphere of radius `r`. It is imparted a horizontal velocity of `sqrt(etagr)`. Find the angle made by the radius vector joining the particle with the vertical at the instant the particle losses contact with the sphere.

Explanation

If v is the speed of the particle when the radius vector makes an angle `theta` with vertical, then
`(cos theta)mg-N=(mv^2)/(r)=m/r[u^2+2gr(1-costheta)]`
When the particle loses contact, `N=0`
`mgcos theta=m/r[(eta+2)gr-2grcostheta]`
`cos theta=(eta+2)-2costheta`
`implies cos theta=(eta+2)//3`