Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii 3 r and 4…

Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is 
  1. 9:16
  2. 16:9
  3. 1:1
  4. 4:3

Solution

Given that m1 m2=43,r1r2=34

Now the total energy of a satellite TE=12mvo2+-GMmr

Since the orbital speed of a satellite vo=GMr

⇒TE=-GMm2r∝mr

⇒TE1TE2=m1 m2·r2r1=43×43=169

Asked in: JEE Main 2022 (27 Jul Shift 1)

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