A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is :

Options

A. `R//2`
B. `R//3`
C. `R//4`
D. `R//5`

Answer

B

Explanation

K.E. = change in gravitational potential energy.
`(1)/(m) ((V_(e))/(2))^(2)=(GMm)/(R+h)+(GMm)/(R )`
`(1)/(2) m ((sqrt(2GM//R))/(2))^(2)=(-GMm)/(R+h)+(GMm)/(R )`
Thus gives `h=(R )/(3)`
Correct choice is (b).