Question

The ratio of the radii of the planets $R_1$ and $R_2$ is $k$. The ratio of the acceleration due to gravity is $r$. The ratio of the escape velocities from them will be

• A. $kr$
• B. $\sqrt{kr}$
• C. $\sqrt{\left(k/r\right)}$
• D. $\sqrt{\left(r/k\right)}$

Answer 1

The correct option is B $\sqrt{kr}$

We know that, $v_e=\sqrt{\left(2gR\right)}$
$\therefore \frac{\left(v_e\right)p_1}{\left(v_e\right)p_2}=\frac{\sqrt{\left(2g_1{R}_1\right)}}{\sqrt{\left(2g_2{R}_2\right)}}=\sqrt{\left(\frac{g_1}{g_2}\right)}\times \sqrt{\left(\frac{R_1}{R_2}\right)}=\sqrt{kr}$