A small block of mass m is pushed on a smooth track from position A with a velocity `2sqrt5` times the minimum velocity required to reach point D. The block will leave the contact with track at the point where normal force between them becomes zero.

At what angle `theta` with horizontal does the block gets separated from the track?

Options

A. `sin^(-2)((1)/(3))`
B. `sin^(-1)((3)/(4))`
C. `sin^(-1)((2)/(3))`
D. never leaves contact with the track

Explanation

`v_1=(2)/(sqrt5)sqrt(5gR)=2sqrt(gR)`
Now `v_2^(2)=v_1^(2)-2g(R+Rsintheta)`
`impliesv_2^2=2gR-2gRsintheta`
`N+mgsintheta=(mv_2^2)/(R), put N=0`
`impliesmgsintheta=m^(2)g(1-sintheta)`
`impliessintheta=(2)/(3)impliestheta=sin^(-1)((2)/(3))`