1. Tardigrade
  2. Question
  3. Physics
  4. 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 vA and vB, respectively, then (vA/vB)=(n/4). The value of n is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $\frac{v_{A}}{v_{B}}=\frac{n}{4}$. The value of $n$ is :

JEE MainJEE Main 2020Gravitation

Solution:

$V_{e} = \sqrt{\frac{2GM}{R}}$ (Escape velocity)
$V_{A} = \sqrt{\frac{2GM}{R}}$
$V_{B} = \sqrt{\frac{2G\left[M/ 2\right]}{R/ 2}} = \sqrt{\frac{2GM}{R}}$
$\frac{V_{A}}{V_{B}} = 1 = \frac{n}{4} \Rightarrow n = 4$