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

3

Explanation

Conservation energy between points A and B
`mg[R/4+R(1- cos theta)]=1/2 mv^(2)`
Also EFD at point B will be give
` mg cos theta=(mv^(2))/R`
`1/4+(1- cos theta) =1/2 cos theta`
`5/4=3/2 cos theta`
`:. cos theta=5/6`