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

C

Explanation

A skier plans …………..
`Delta h = (R )/(4)+ R(1-cos theta)`
`(1)/(2)mv^(2)= mg Delta h = (mgR)/(4) {1+4(1-cos theta)}`

`:. (mv^(2))/(R ) = (mg)/(2) (5-4 cos theta)`
`mg cos theta - N = (mv^(2))/(R )`

`mg cos theta = (mg)/(2)(5-4cos theta)`
`cos theta = 5//6`