Correct formula for height of a satellite from earths surface is :

Solution

Physics sir · 4 steps

Let gravity supply the centripetal force, swap GM for gR², take a cube root, then subtract R.

1. Force balance. A satellite at distance r = R + h from the centre of the earth moves in a circle. Gravity provides the centripetal force, so GMm/r² = m r ω² with ω = 2π/T.
2. Replace GM. At the surface g = GM/R², so GM = gR². This gives r³ = GMT²/4π² = gR²T²/4π².

   h = r - R = ((T² R² g)/4π²)^(1/3) - R

3. Units check. T²R²g has units s² × m² × m s⁻² = m³. Its cube root is a length, as a height must be.
4. So. The height of the satellite above the surface is given by option (a).

The idea to keep. For any orbit question, start from GMm/r² = mrω², write GM = gR², and remember that r is measured from the centre. Subtract R only when the question asks for height.

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