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JEE MainPhysicsGravitation

Two satellites A and B of masses m and 3m respectively are to be placed in circular orbits around the Earth. If a student plots the expected orbital speed v against the orbital radius r for both satellites, which of the following correctly describes the resulting graphs?

Options

  1. ATwo distinct decreasing curves, where the curve for satellite B lies above the curve for satellite A.
  2. BA single coincident curve for both satellites, which decreases non-linearly and is concave upwards.
  3. CTwo distinct decreasing curves, where the curve for satellite B lies below the curve for satellite A.
  4. DA single coincident straight line for both satellites, having a negative slope.

Correct answer

B. A single coincident curve for both satellites, which decreases non-linearly and is concave upwards.

Step-by-step solution

The orbital speed of a satellite in a circular orbit is given by v = GM r , where M is the mass of the Earth and r is the orbital radius. This formula shows that the orbital speed is independent of the mass of the satellite. Therefore, both satellites A and B will have the exact same relationship between v and r , meaning their graphs will coincide into a single curve. Furthermore, the relationship is v r^ -1/2 . This represents a non-linear decreasing curve. Since d^2v dr^2 > 0 , the curve is concave upwards. Thus

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