Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.
If T A and T B are the time periods of A and B respectively then the value of T B - T A :
[Given : radius of earth = 6400 km, mass of earth = 6 × 10²⁴ kg]

Solution

Physics sir · 3 steps

Period depends only on orbit radius, so ignore the masses and measure r from Earth's centre.

1. Masses drop out. Gravity supplies the centripetal force: GMm/r² = mω² r. The satellite mass m cancels, so 200 kg and 400 kg play no part.

   T = 2π√(r³/GM), r = R + h

   Satellite	r = R + h	r^(3/2)	T
   A	7.0 × 10⁶ m	1.852 × 10¹⁰	≈ 5817 s
   B	8.0 × 10⁶ m	2.263 × 10¹⁰	≈ 7107 s

2. Put in numbers. GM = 6.67 × 10⁻¹¹ × 6 × 10²⁴ = 4.0 × 10¹⁴ m³ s⁻², so √GM = 2.0 × 10⁷. Then T_B - T_A = 2π/√GM(r_B^(3/2) - r_A^(3/2)) = (6.283 × 4.11 × 10⁹)/(2.0 × 10⁷).
3. So. T_B - T_A ≈ 1.29 × 10³ s. The nearest option is (a), 1.33 × 10³ s. The other options are far from this value.

The idea to keep. Orbital period never depends on the satellite's mass. Always add the Earth's radius to the height before using T² ∝ r³.

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