The ratio of the radius of a planet A to that | vedclass

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(C) The formula for escape velocity is given by $v_e = \sqrt{2gR}$,where $g$ is the acceleration due to gravity and $R$ is the radius of the planet.Gi

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$\sqrt{rx}$

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(C) The formula for escape velocity is given by $v_e = \sqrt{2gR}$,where $g$ is the acceleration due to gravity and $R$ is the radius of the planet.Given the ratio of radii $\frac{R_A}{R_B} = r$ and the ratio of acceleration due to gravity $\frac{g_A}{g_B} = x$.The ratio of escape velocities is $\frac{v_A}{v_B} = \sqrt{\frac{2g_A R_A}{2g_B R_B}} = \sqrt{\frac{g_A}{g_B} 	imes \frac{R_A}{R_B}}$.Substituting the given ratios,we get $\frac{v_A}{v_B} = \sqrt{x 	imes r} = \sqrt{rx}$.

The ratio of the radius of a planet $A$ to that of planet $B$ is $r$. The ratio of acceleration due to gravity on the planets is $x$. The ratio of the escape velocities from the two planets is

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