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JEE Main 2023 (1 Feb, Shift 2) · Escape Velocity

Escape Velocity question from JEE Main 2023 (1 Feb, Shift 2)

Q30JEE Main 2023 · 1 FEB · SHIFT 2Medium

Escape Velocity

The escape velocities of two planets $\text{A}$ and $\text{B}$ are in the ratio $1 : 2$ . If the ratio of their radii respectively is $1 : 3$ , then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:

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Answer: (c)

$v_e = \sqrt{2gR} \Rightarrow g = \frac{v_e^2}{2R}$ .
$\frac{g_A}{g_B} = \left(\frac{v_A}{v_B}\right)^2\frac{R_B}{R_A} = \frac{1}{4}\times\frac{3}{1}$ .
$\frac{g_A}{g_B} = \frac{3}{4}$ .
So the answer is (c) $\frac{3}{4}$ .

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