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 $v=\sqrt{2gR}$
For escape velocity of the body from the platform potential energy $+$ kinetic energy $=0$
$-\frac{GMm}{2R}+\frac{1}{2}m{v}^2=0$
$\Rightarrow f{v}_{\text{escape }}=\sqrt{\frac{GM}{R^2}\cdot R}=\sqrt{gR}=fv$
From the surface of the earth, $v_{\text{escape }}=\sqrt{2gR}$
$\therefore f{v}_{\text{escape }}=\frac{v_{\text{escape }}}{\sqrt{2}}.$
$\therefore f=\frac{1}{\sqrt{2}}$