Question

The ratio of the radii of the planets $P_1$ and $P_2$ is $a$. The ratio of their acceleration due to gravity is $b$. The ratio of the escape velocity from them will be :

• A. $ab$
• B. $\sqrt{ab}$
• C. $\sqrt{a/b}$
• D. $\sqrt{b/a}$

Answer 1

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

We have,

$V_1=\sqrt{2g_1{R}_1}$

$V_2=\sqrt{2g_2{R}_2}$

$\Rightarrow \frac{V_1}{V_2}=\sqrt{\frac{g_1}{g_2}.\frac{R_1}{R_2}}$

$=\sqrt{a.b}$

Hence,

Option $B$ is correct.