Question

There are two planets. The ratio of radius of the two planets is $k$ but ratio of acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocity?

• A. $(kg{)}^{1/2}$
• B. $(kg{)}^{-1/2}$
• C. $(kg{)}^2$
• D. $(kg{)}^{-2}$

Answer 1

The correct option is A $(kg{)}^{1/2}$

The equation of escape velocity is $v_e=\sqrt{2gr}$

so, $\frac{v_{e}1}{v_{e}2}=\frac{\sqrt{2g_1{r}_1}}{\sqrt{2g_2{r}_2}}=\sqrt{kg}$