Question

The ratio of the radii of planets A and B is $K_1$ and ratio of accelerations due to gravity on them is $K_2$ The ratio of escape velocities from them will be:

• A. $K_1{K}_2$
• B. $\sqrt{K_1{K}_2}$
• C. $\sqrt{\frac{K_1}{K_2}}$
• D. $\sqrt{\frac{K_2}{K_1}}$

Answer 1

The correct option is B $\sqrt{K_1{K}_2}$

Escape speed is, $v_e=\sqrt{2gR}$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{g_1{R}_1}{g_2{R}_2}}$
It is given, $\frac{R_1}{R_2}=K_1$ and $\frac{g_1}{g_2}=K_2$
$\Rightarrow \frac{v_1}{v_2}=\sqrt{K_1{K}_2}$