Question

The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the earth. The escape velocity of a body from this platform is $fv$, where $v$ is its escape velocity from the surface of the Earth. The value of $f$ is :-

• A. 1/2
• B. $\sqrt 2 $
• C. $ \frac{1}{\sqrt 2} $
• D. 1/3

Answer 1

Answer: (C)

Escape velocity of the body from the surface of earth is $v=\sqrt{2 g R}$
For escape velocity of the body from the platform potential energy $+$ kinetic energy $=0$
$-\frac{G M m}{2 R}+\frac{1}{2} m v^{2}=0 $
$\Rightarrow f v_{\text {escape }}=\sqrt{\frac{G M}{R^{2}} \cdot R}=\sqrt{g R}=f v$
From the surface of the earth, $v_{\text {escape }}=\sqrt{2 g R}$
$\therefore f v_{\text {escape }}=\frac{v_{\text {escape }}}{\sqrt{2}} . $
$ \therefore f=\frac{1}{\sqrt{2}} $