A satellite of 10³ kg mass is revolving in circular orbit of radius 2R. If (10⁴R/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)
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Question

A satellite of 10³ kg mass is revolving in circular orbit of radius 2R. If (10⁴R/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)

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G1 Physics · Accepted Answer

Initial total energy: Eᵢ = -GMm/[2(2R)] = -GMm/(4R) After adding energy ΔE = 10⁴R/6: -GMm/(4R) + 10⁴R/6 = -GMm/(2r) Using: GM = gR² m = 10³ kg g = 10 m/s² So: GMm = 10⁴R² Substituting: -10⁴R/4 + 10⁴R/6 = -10⁴R²/(2r) Divide by 10⁴R: -1/4 + 1/6 = -R/(2r) -1/12 = -R/(2r) Therefore: r = 6R