Question

A body is projected up from the surface of the earth with a velocity equal to $( \frac{3}{4}th )$ of its escape velocity. If $R$ be the radius of earth, the height it reaches is

• A. $ \frac{3R}{10} $
• B. $ \frac{9R}{7} $
• C. $ \frac{8R}{5} $
• D. $ \frac{9R}{5} $

Answer 1

Answer: (B)

If body is projected with velocity $\left(v < v_{e}\right)$,
then height upto which it will rise,
$h=\frac{R}{\frac{v_{e}^{2}}{v^{2}}-1}$
$v=\frac{3}{4} v_{e}$ (given)
$\therefore h=\frac{R}{\frac{v_{e}^{2}}{\frac{9}{16} v_{e}^{2}}-1}$
$=\frac{9}{7} R$