Question

The escape velocity from a planet is $v_o$. The escape velocity from another planet having twice the radius, but of same density will be -

• A. $0.5v_0$
• B. $v_0$
• C. $2v_0$
• D. $4v_0$

Answer 1

The correct option is C $2v_0$

We know, escape velocity,

$v_e=\sqrt{\frac{2GM}{R}}$

$\Rightarrow v_e=\sqrt{\frac{2G\times \frac{4\pi \rho R^3}{3}}{R}}$

$\Rightarrow v_e=\sqrt{\frac{8G\pi \rho R^2}{3}}$

$\Rightarrow v_e\propto R$

So, if radius is doubled keeping density same, the escape velocity gets doubled.

Therefore, the escape velocity from another planet will be $2v_o$.