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COMEDK2023PhysicsGravitation

If escape velocity on earth surface is 11.1 kmh ⁻¹ , then find the escape velocity on moon surface. If mass of moon is 1 81 times of mass of earth and radius of moon is 1 4 times radius of earth.

Options

  1. A2.46 kmh ⁻¹
  2. B3.46 kmh ⁻¹
  3. C4.4 kmh ⁻¹
  4. DNone of these

Correct answer

A. 2.46 kmh ⁻¹

Step-by-step solution

Given, Escape velocity on the surface of the earth is given by i.e. v_ = 2 g R_e Mass of the moon, M_m= M_e 81 Radius of the moon, R_m= R_e 4 Escape velocity on the surface of the moon v_m= 2 G M_m R_m = 2 G ( M e 81 ) R_e 4 = 2 2 9 G M_e R_e From Eq. (i), = 2 9 2 G M_e R_e = 2 9 v_e Escape velocity v_e=11.1 ~km / h = 2 9 11.1=2.46 ~km ~h ⁻¹

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