A body is projected up with a velocity equal to `3//4th` of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth is `R`)

Options

A. `(3R)/(10)`
B. `(9R)/(7)`
C. `(8R)/(5)`
D. `(9R)/(5)`

Answer

B

Explanation

Apply C.O.M.E.
`(1)/(2) mV^(2) = (mgh)/(( 1 + (h)/(R)))`
V = `(3)/(4) V_(e) = (3)/(4) sqrt(2gR) (V_(e) = sqrt(2gR))`
`(1)/(2) xx (9)/(16) xx 2g R = (gh)/( 1 + (h)/(R)) implies h = (9R)/(7)`