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, $h=\frac{R}{\frac{v_e^2}{v^2}-1}$
$v=\frac{v_e}{2}$ (given) $\therefore h=\frac{R}{{\left(\frac{v_e}{\frac{v_2}{2}}\right)}^2-1}=\frac{R}{4-1}=\frac{R}{3}$