Q 11-07-077JEE MainJEE Main 2024 (31 Jan, Shift 2)Easy
The mass of the moon is $\dfrac1{144}$ times the mass of a planet and its diameter $\dfrac1{16}$ times the diameter of the planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be:
Answer: (A) $\dfrac v3$
$v_e = \sqrt{\dfrac{2GM}{R}} \propto \sqrt{\dfrac MR}$:
$$v_m = v\sqrt{\frac{1/144}{1/16}} = v\sqrt{\frac19} = \frac v3$$
Solution by Sreeraj P, M.Sc Physics