A small body of mass m slides without friction from the top of a hemisphere of radius r. At what height will the body be detached from the surface of hemisphere?

Options

A. `h=(r)/(2)`
B. `h=(r)/(3)`
C. `h=(2r)/(3)`
D. `h=(r)/(4)`

Answer

C

Explanation

When released from top with zero velocity block leaves contact at

`costheta=(2)/(3)`
`because"In" Delta"AOB`,
`costheta=(OA)/(AB)rArrcostheta=(h)/(r)`
`therefore" "h=rcostheta=(2r)/(3)`