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`
B. `h=r//2`
C. `h=r//3`
D. `2r//3`

Answer

C

Explanation

Fromfigure,
`g cos theta=(v^2)/(r)`
`v^2=grcostheta`
`costheta=(r-h)/(r)`
`therefore" "v^2=gr((r-h))/(r)=g(r-h)" "....(i)`
By third kinematical equation of motion
`v^2 =2gh" "…(ii)`
From Eqs.(i) and (ii) `g(r-h)=2gh`
`therefore " "h=(r)/(3)`