Question

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

• A. R/3
• B. R/2
• C. R/4
• D. R/5

Answer 1

The correct option is A

R/3

If body is projected with velocity v $v<v_e$ then height up to which it will rise, $h=\frac{R}{\frac{v_e^2}{v^2}-1}$
$v=\frac{v_e}{2}\left(given\right)\therefore h=\frac{R}{(\frac{v_e}{\frac{v_e}{2}}{)}^2-1}=\frac{R}{4-1}=\frac{R}{3}$