A satellite of 10³ kg mass is revolving in circular orbit of radius 2 R. If (10⁴ R)/6 J energy is supplied to the satellite, it would revolve in a new circular orbit of radius
(use g=10 m / s², R= radius of earth)

Solution

Physics sir · 4 steps

Write the total energy in both orbits; the energy you supply is exactly the difference between them.

1. Energy in orbit. A satellite in a circular orbit of radius r has total energy E = -GMm/2r. Use GM = gR², so E = -(gR² m)/2r. With g = 10 m s⁻² and m = 10³ kg, gm = 10⁴.
2. Old orbit. At r = 2R: E₁ = -(10⁴ R²)/(2 × 2R) = -2500R J.
3. Add the energy. Supplied energy is (10⁴ R)/6 ≈ 1666.7R J. So E₂ = -2500R + (10⁴ R)/6 = -(10⁴ R)/12 ≈ -833.3R J. The energy rises but stays negative, so the satellite is still bound.

   -(10⁴ R²)/2r = -(10⁴ R)/12 ⇒ r = 6R

4. So. The new circular orbit has radius 6R, which is option (b).

The idea to keep. For orbit transfer questions, use total energy -GMm/2r, not potential energy alone. Replace GM with gR² and let the numbers do the work.

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