The minimum speed with which a body must be thrown to reach a height of `(R )/(4)` above the surface of earth is :

Options

A. `sqrt(g (R )/(2))`
B. `sqrt(gR)`
C. `sqrt((2)/(5)gR)`
D. `sqrt(g(R )/(5))`.

Answer

C

Explanation

Here `(1)/(2)mv^(2)=U_(2)-U_(1)=(-GMm)/((5)/(4)R)-((-GMm)/(R ))`
`rArr v=sqrt((2GM)/(5R))=sqrt((2)/(5R)*gR^(2)) = sqrt((2)/(5)gR)`
Thus correct choice is (c ).