Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is

Solution

Physics sir · 3 steps

Orbital speed depends only on the orbit radius, so forget the satellite masses and compare 1/√r.

1. Gravity gives centripetal force. For a satellite of mass m in a circular orbit of radius r, gravity supplies the centripetal force: GMm/r² = mv²/r. The satellite's mass m appears on both sides and cancels.

   v = √(GM/r) ⇒ v ∝ 1/√r

2. Take the ratio. Here M is the earth's mass, the same for both. So v₁/v₂ = √(r₂/r₁) = √(3r/r) = √3.
3. So. The ratio of orbital speeds is √3 : 1, which is option (b). The masses m and 3m play no part.

The idea to keep. Orbital speed v = √(GM/r) does not depend on the satellite's own mass. A satellite in a larger orbit moves slower, as 1/√r.

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