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 $2v_0$

The escape velocity of the planet is given by,

$v_0=\sqrt{\frac{2G{M}_e}{R_e}}=\sqrt{\frac{2G\rho \frac{4}{3}\pi R_e^3}{R_e}}$

$\because \text{Mass}\left(M\right)=V\times \rho =\frac{4}{3}\pi R^3\times \rho$

So, $v_0=\sqrt{2G\rho \frac{4}{3}\pi R_e^2}$

Escape velocity of the planet of twice the radius,

$v^{\prime }=\sqrt{2G\rho \frac{4}{3}\pi (2R_e{)}^2}=2v_0$