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COMEDK202510 May 2025Morning ShiftPhysicsGravitationActual

A planet is 121 times heavier than moon and has a diameter 9 times that of moon. If the escape velocity on the planet is v , then the escape velocity on the moon will be:

Options

  1. A33 v 8
  2. B3 v 11
  3. C8 v 33
  4. D11 v 3

Correct answer

B. 3 v 11

Step-by-step solution

The escape velocity v_e of a body is given by the formula v_e = 2GM R , where M is the mass and R is the radius of the body. Let M_p and R_p be the mass and radius of the planet, and M_m and R_m be the mass and radius of the moon. Given M_p = 121 M_m and the diameter D_p = 9 D_m , which implies R_p = 9 R_m . The escape velocity on the planet is v = 2GM_p R_p . The escape velocity on the moon is v_m = 2GM_m R_m . Taking the ratio of the escape velocities: v_m v = M_m R_m R_p M_p = M_m R_m 9 R_m 121 M_m = 9 121 = 3 1

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