A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to 1/3rd the escape velocity for the planet. The maximum height attained by the body is

Options

A. `R//2`
B. `R//3`
C. `R//5`
D. `R//9`

Answer

D

Explanation

Let `h` be the maximum height attained, then from equation of the motion
`v^(2)=u^(2)+2gh`
when `u=0rArrv=sqrt(2gh)`
Given, `v=(v_(e))/(3)`, where, `v_(e)=sqrt(2gR)rArr sqrt(2gh)=(1)/(3)sqrt(2gR)`
On squaring both sides of equation, we get
`h=(R)/(9)`