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Q. The escape velocities of two planets A and 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 :

JEE MainJEE Main 2023Gravitation

Solution:

Ve=2GMR=2Gρ43πR3R=CρR
Ve1Ve2=R1R2ρ1ρ2=12
R21R22×ρ1ρ2=14
R1R2=13
g=GM2R2=G43πR3×ρR2CρR
g1g2=ρ1R1ρ2R2=14R22R21×R1R2
=14×R2R1=34