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JEE Main20231 Feb 2023Evening ShiftPhysicsGravitationActual

The escape velocities of two planets A a n d 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:

Options

  1. A4 3
  2. B3 2
  3. C2 3
  4. D3 4

Correct answer

D. 3 4

Step-by-step solution

The formula to calculate the mass M of any planet of radius R and density ρ , considering it to be a sphere, is given by M =   4 3 π R 3 ρ . . . . . . . . . . . . . . . . . . . . . ( 1 ) The escape velocity v A for planet A can be expressed as V A = 2 G M A R A = 2 G ρ A 4 3 π R A 3 R A = C ρ A . R A . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 ) where, G is Gravitational constant and C =   8 π G 3 is a constant. Similarly, the escape velocity v B of plane

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