The ratio of the radii of planets A and B is | vedclass

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(B) The escape velocity $v$ from the surface of a planet is given by the formula $v = \sqrt{2gR}$,where $g$ is the acceleration due to gravity and $R$

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$\sqrt {{k_1}{k_2}}$

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(B) The escape velocity $v$ from the surface of a planet is given by the formula $v = \sqrt{2gR}$,where $g$ is the acceleration due to gravity and $R$ is the radius of the planet.Given that the ratio of the radii is $\frac{R_A}{R_B} = k_1$ and the ratio of acceleration due to gravity is $\frac{g_A}{g_B} = k_2$.Therefore,the ratio of the escape velocities $v_A$ and $v_B$ is:$\frac{v_A}{v_B} = \frac{\sqrt{2g_A R_A}}{\sqrt{2g_B R_B}} = \sqrt{\frac{g_A}{g_B} 	imes \frac{R_A}{R_B}}$Substituting the given ratios:$\frac{v_A}{v_B} = \sqrt{k_2 	imes k_1} = \sqrt{k_1 k_2}$.

The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and the ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be

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