The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be
The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be
${k_1}{k_2}$
$\sqrt {{k_1}{k_2}} $
$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $
$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $
The ratio of the radii of planets $A$ and $B$ is ${k_1}$ and ratio of acceleration due to gravity on them is ${k_2}$. The ratio of escape velocities from them will be
$v = \sqrt {2gR} $
$⇒ \frac{{{v_A}}}{{{v_B}}} = \sqrt {\frac{{{g_A}}}{{{g_B}}} \times \frac{{{R_A}}}{{{R_B}}}} = \sqrt {{k_1} \times {k_2}} = \sqrt {{k_1}{k_2}} $
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