Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be

Solution

Physics sir · 3 steps

In the same orbit, gravity fixes the speed; the satellite's own mass cancels out completely.

1. Gravity gives centripetal force. For a satellite of mass m in a circular orbit of radius r, the earth's pull supplies the centripetal force: GMm/r² = mv²/r.

   v = √(GM/r)

2. Mass cancels. The satellite's mass m cancels from both sides, so v depends only on the earth's mass M and the radius r. Same orbit means same r, so A and B move with the same speed.

   Quantity	Expression	A compared with B
   Potential energy	-GMm/r	twice as large in size
   Kinetic energy	GMm/2r	twice as large
   Total energy	-GMm/2r	twice as large in size
   Speed	√(GM/r)	same

3. So. Every energy carries a factor of m and doubles for A, but the speed has no m in it. The answer is (d), speed.

The idea to keep. Orbital speed, period and angular speed depend only on the planet's mass and the orbit radius. Every energy of the satellite scales with its own mass.

Answer from the NTA final answer key. Solution by PrepWiser.