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MHT CET202613 April 2026Evening ShiftPhysicsGravitationActual

If earth has a mass nine times and radius twice to the planet P. Then v_e 3 x ms ⁻¹ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where v_e is escape velocity on earth. The value of x is

Options

  1. A2
  2. B3
  3. C18
  4. D1

Correct answer

A. 2

Step-by-step solution

The escape velocity on Earth is given by v_e = 2GM_e R_e The escape velocity on planet P is given by v_p = 2GM_p R_p Given that M_e = 9M_p M_p = M_e 9 and R_e = 2R_p R_p = R_e 2 Substituting these values into the expression for v_p : v_p = 2G ( M_e 9 ) R_e 2 v_p = 2GM_e R_e 2 9 v_p = 2GM_e R_e 2 3 v_p = v_e 3 2 Comparing this with the given expression v_e 3 x , we get x = 2 . Answer: 2

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