Two satellites A and B, having masses in the ratio 4: 3, are revolving in circular orbits of radii 3 r and 4 r respectively around the earth. The ratio of total mechanical energy of A to B is :

Solution

Physics sir · 4 steps

Total energy goes as m/r, so multiply the mass ratio by the inverted radius ratio.

1. Energy in orbit. For a satellite of mass m in a circular orbit of radius r, the kinetic energy is GMm/2r and the potential energy is -GMm/r. Adding them gives the total energy.

   E = -GMm/2r

2. Take the ratio. G, M, the factor 2 and the minus sign are the same for both satellites, so they cancel. That leaves E_A/E_B = m_A/m_B × r_B/r_A.
3. Put in numbers. E_A/E_B = 4/3 × 4r/3r = 16/9.
4. So. The ratio of total mechanical energy of A to B is 16 : 9, option (b). Both energies are negative, so their ratio is positive.

The idea to keep. For circular orbits, E = -GMm/2r: energy is proportional to mass and inversely proportional to radius. Write the ratio first, then put in numbers.

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