Q 11-07-162JEE MainJEE Main 2020 (9 Jan, Shift 2)Easy
Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the Planets $A$ and $B$ are $v_A$ and $v_B$, respectively, then $\dfrac{v_A}{v_B} = \dfrac{n}{4}$. The value of $n$ is:
Answer: (A) $4$
$v_e = \sqrt{\dfrac{2GM}{R}}$ depends only on $M/R$, which is the same for both planets. So $\dfrac{v_A}{v_B} = 1 = \dfrac{n}{4}$ and $n = 4$.
Solution by Sreeraj P, M.Sc Physics