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)

$V_{e}=\sqrt{\frac{2 G M}{R}}=\sqrt{\frac{2 G \frac{4}{3} \pi R^{3} \rho}{R}}$
$ \Rightarrow V_{e} \propto R$
$\therefore \frac{V'}{V}=\frac{4 R}{R}$
$ \Rightarrow V^{'}=4 V$