question_answer

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 \[{{\text{v}}_{A}}\]and\[{{\text{v}}_{B}}\], respectively, then\[\frac{{{\text{v}}_{A}}}{{{\text{v}}_{B}}}=\frac{n}{4}\]. [JEE MAIN Held on 09-01-2020 Evening]

A)  1                    

B)       4

C)  3                     D)       2 Correct Answer: B Solution : [b] \[V=\sqrt{\frac{2GM}{R}}\]

\[\frac{{{V}_{1}}}{{{V}_{2}}}=\sqrt{\frac{{{M}_{1}}{{R}_{2}}}{{{M}_{2}}{{R}_{1}}}}\]