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NEETPhysicsGravitation

The escape velocity on the surface of planet A is 4 times the escape velocity on the surface of planet B . If the mass of planet A is 8 times the mass of planet B , then the ratio of their radii ( R_A R_B ) is :

Options

  1. A2
  2. B1 4
  3. C1 2
  4. D4

Correct answer

C. 1 2

Step-by-step solution

The escape velocity of a planet is given by v = 2GM R . Taking the ratio of the escape velocities for planets A and B : v_A v_B = M_A M_B R_B R_A We are given that v_A v_B = 4 and M_A M_B = 8 . Substituting these values into the equation gives: 4 = 8 R_B R_A Squaring both sides: 16 = 8 R_B R_A R_B R_A = 16 8 = 2 Therefore, the ratio of their radii is: R_A R_B = 1 2 Answer: 1 2

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