Question

The ratio of the radii of the planets $P_1$ and $P_2$ is $2:1$ and the ratio of their acceleration due to gravity is $3:1$. Then the ratio of the escape velocities from them well be

• A. $6$
• B. $\sqrt{6}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is B $\sqrt{6}$

$\frac{g_1}{g_2}=\frac{3}{1}$ (given)

and $\frac{R_1}{R_2}=\frac{2}{1}$ (given)

we know that escape velocity

$V_{11}=\sqrt{2g_1{R}_1}{V}_{12}=\sqrt{2g_2{R}_2}$

The ratio's $=\frac{V_{11}}{V_{12}}=\frac{\sqrt{2g_1{R}_1}}{\sqrt{2g_2{R}_2}}$

$=\sqrt{\frac{3\times 2}{1\times 1}}=\sqrt{\frac{6}{1}}=\sqrt{6}$ (Option B)