A skier plane to ski a smooth fixed hemisphere of radius `R` . He starts from rest from a curve 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

At the time of leaving contact

`N=0`
:. `mgcostheta=(mv^(2))/(R)=(m(2gh))/(R)`
:. `costheta=(2h)/(R)=([(R)/(4)+R(1-costheta)])/(R)`
On solving this equation, we get
`costheta=5//6` or `theta=cos^(-1)((5)/(6))`