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MHT CET202123 Sep 2021Evening ShiftPhysicsGravitationActual

The radius of planet is twice the radius of the earth. Both have almost equal average mass densities. If ' V_P ' and ' V_E ' are escape velocities of the planet and the earth respectively, then

Options

  1. AV _ E =1.5 ~V _ P
  2. BV _ P =1.5 ~V _ E
  3. CV _ P =2 ~V _ E
  4. DV _ E =3 ~V _ P

Correct answer

C. V _ P =2 ~V _ E

Step-by-step solution

aligned & Escape velocity v= 2 G M R & M= 4 3 R^3 & v= 2 G 4 3 R^3 R = 8 G 3 R^2 =R 8 G 3 & v R & If is constant, the v R & v_P v_E = R_P R_E =2 & v_P=2 v_E aligned

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