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JEE MainPhysicsGravitation

Two satellites P and Q , having masses m and 3m respectively, are revolving in circular orbits around a planet. If the orbital speeds of both the satellites are equal, which of the following physical quantities must also be identical for them?

Options

  1. ATime period of revolution
  2. BKinetic energy
  3. CAngular momentum
  4. DCentripetal force

Correct answer

A. Time period of revolution

Step-by-step solution

The orbital speed of a satellite is given by v = GM r , where M is the mass of the planet and r is the orbital radius. Since both satellites have the same orbital speed, their orbital radii r must be equal. The time period of revolution is T = 2 r v . Since both r and v are identical for the two satellites, their time periods must also be equal. The other quantities depend on the mass of the satellite: Kinetic energy K = 1 2 mv^2 Angular momentum L = mvr Centripetal force F = mv^2 r Because their masses are differe

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