JEE Main 2024 · 8 April · evening · Single correct · +4 / −1

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3 v, the speed of B will be :

  1. (a) 6 v
  2. (b) 4/3 v
  3. (c) 3 v
  4. (d) 12 v
Answer and solution

Answer (a) 6 v

Solution

Physics sir · 3 steps

Orbital speed goes as 1/√r, so the inner satellite, four times closer, moves twice as fast.

  1. Orbital speed. Gravity supplies the centripetal force: GMm/r² = mv²/r. The satellite's own mass m cancels.

    v₀ = √(GM/r) ⇒ v_B/v_A = √(r_A/r_B)

  2. Put in numbers. v_B/v_A = √(4R/R) = √4 = 2. With v_A = 3v, this gives v_B = 2 × 3v = 6v.
  3. So. Satellite B, in the smaller orbit, moves at 6v. The answer is (a).

The idea to keep. For circular orbits around the same planet, v ∝ 1/√r. Closer orbits are faster, and the speed changes by the square root of the radius ratio, not the ratio itself.

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

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Asked about 160 times in JEE Main since 2020. This question is from 2024.