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

Question

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, 9 : 16, 16 : 9, 1 : 1, 4 : 3

MARKS App · Accepted Answer

Given that m 1 m 2 = 4 3 , r 1 r 2 = 3 4 Now the total energy of a satellite T E = 1 2 m v o 2 + - G M m r Since the orbital speed of a satellite v o = G M r ⇒ T E = - G M m 2 r ∝ m r ⇒ T E 1 T E 2 = m 1 m 2 · r 2 r 1 = 4 3 × 4 3 = 16 9

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