Question

The escape velocity from a planet is $v_0$. The escape velocity from a planet having twice the radius but same density will be

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

Answer 1

The correct option is C $2v_0$

Escape velocity velocity
$v_0=\sqrt{\frac{2G{M}_e}{R_e}}=\sqrt{\frac{2G\rho \frac{4}{3}\pi R_e^3}{R_e}}$
$v_0=\sqrt{2G\rho \frac{4}{3}\pi R_e^2}$
$v_0\propto R_e$
If the radius is doubled, then the escape velocity is
$v^{\prime }=2v_0$.