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Manipal MET2022PhysicsGravitation

If the radius of a planet is three times the radius of the earth. Both have same mass-densities. v_P and v_E are the escape velocities of the planet and the earth respectively, then

Options

  1. Av_P=1.5 v_E
  2. Bv_P=3 v_E
  3. Cv_E=2 v_P
  4. Dv_P=2 v_E

Correct answer

B. v_P=3 v_E

Step-by-step solution

The escape velocity of a planet is given by, v= 2 G M R = 2 G R 4 3 R^3 V R v_P v_E = R_P _P R_E _E = R_P R_E ( _P= _E ) v_P v_E = 3 R_E R_E =3 ( R_P=3 R_E ) v_P=3 v_E

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