A skier plans to ski a smooth fixed hemisphere of radius R He starts from rest from a curved smooth surface of height (R/4) the angle `theta` at which he leaves the hemisphere is

Options

A. `cos^(-1)(2//3)`
B. `cos^(-1)(5//sqrt(3)`
C. `cos^(-1)(5//6)`
D. `cos^(-1)(5//2sqrt(3)`

Answer

C

Explanation

Conserving energy between points A&B
`mg[R/4+R(1-costheta)]=1/2mv^(2)`
also efd at point B will give
` mg costheta =(mv^(2))/R`
`1/4+(1-costheta) =1/2costheta`
`5/4=3/2costheta`
`costheta =5/6`