A body is fired with a velocity of magnitude `sqrt(gR) lt V lt sqrt(2gR)` at an angle of `30^(@)` with the radius vector of earth. If at the highest point the speed of the body is `V//4`, the maximum height attained by the body is equal to:

Options

A. `v^(2)//8g`
B. `R`
C. `sqrt(2)R`
D. None of the above

Explanation

As the force acting between the body and the earth passes through the centre of the earth. Angular momentum of the system is conserved about the centre of earth. And the velocity at the highest point of the trajectory is perpendicular to the radius vector.
So, by conservation of momentum about the centre of earth.
`mv sin 30^(@).R=(mv)/(4)(R+h)`
`(R )/(2)=(R+h)/(4)rArrh=R`