COMEDK2023Morning ShiftPhysicsGravitationActual
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
- A4.4 ~kmh ⁻¹
- B2.47 ~kmh ⁻¹
- CNone of these
- D3.46 ~kmh ⁻¹
Correct answer
B. 2.47 ~kmh ⁻¹
Step-by-step solution
The escape velocity v_e from the surface of a planet is given by the formula v_e = 2GM R , where M is the mass of the planet and R is its radius. Let M_e and R_e be the mass and radius of the Earth, and M_m and R_m be the mass and radius of the Moon. Given M_m = M_e 81 and R_m = R_e 4 . The escape velocity on the Moon v_m is given by v_m = 2GM_m R_m . Substituting the given ratios into the expression for v_m : v_m = 2G(M_e/81) R_e/4 = 2GM_e R_e 4 81 = 2GM_e R_e 4 81 . Since v_e = 2GM_e R_e = 11.1 km/h , we have v_m