Question

The ratio of the radius of a planet A to that of planet B is $r$. The ratio of accelerations due to gravity for the two planets is $x$. The ratio of the escape velocities from the two planets is :

• A. $\sqrt{rx}$
• B. $\sqrt{\frac{r}{x}}$
• C. $\sqrt{r}$
• D. $\sqrt{\frac{x}{r}}$

Answer 1

The correct option is A $\sqrt{rx}$

Escape Velocity is given by: $V_e=\sqrt{2gR}$
Given: $\frac{R_A}{R_B}=r$ and $\frac{g_A}{g_B}=x$
Taking ratio of the escape velocities of the $2$ planets:
$\frac{V_A}{V_B}=\sqrt{rx}$