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Question 5

Two satellites $$A$$ and $$B$$ move round the earth in the same orbit. The mass of $$A$$ is twice the mass of $$B$$. The quantity which is same for the two satellites will be

$$\frac{G M_E m}{r^2} = \frac{m v_0^2}{r} \implies v_0 = \sqrt{\frac{G M_E}{r}}$$

$$\text{Orbital speed } v_0 \text{ is independent of the satellite's mass } m \text{, so it remains identical for both } A \text{ and } B.$$

$$K = \frac{G M_E m}{2r}, \quad U = -\frac{G M_E m}{r}, \quad E = -\frac{G M_E m}{2r}$$

Since $$m_A = 2m_B$$, the kinetic, potential, and total energies of satellite A are twice those of satellite B

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