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Question: Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of...

Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A to B is

A

1 : 3

B

3 : 1

C

3 : 4

D

12 : 1

Answer

12 : 1

Explanation

Solution

Total mechanical energy of satellite

E=−GMm2rE = \frac { - G M m } { 2 r }⇒ EAEB=mAmB×rBrA\frac { E _ { A } } { E _ { B } } = \frac { m _ { A } } { m _ { B } } \times \frac { r _ { B } } { r _ { A } }⇒31×4rr\frac { 3 } { 1 } \times \frac { 4 r } { r }=121\frac { 12 } { 1 }