Question

The escape velocity from the Earth's surface is $v$. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

• A. v
• B. 2 v
• C. 3 v
• D. 4 v

Answer 1

Answer: (D)

$V_e=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G\frac{4}{3}\pi R^3\rho }{R}}$
$\Rightarrow V_e\propto R$
$\therefore \frac{V^{\prime }}{V}=\frac{4R}{R}$
$\Rightarrow V^{{}^{\prime }}=4V$