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Two satellites A and B, ratio of mass 3:1 are in circular orbit r and 4r. Then the ratio of the total mechanical energy of A to B is:

Option: 1

1:3


Option: 2

3:1


Option: 3

1:12


Option: 4

12:1


Answers (1)

best_answer

As we learn

Energy of satellite -

K=\frac{1}{2}mV^{2}=\frac{GMm}{2r}

U=-\frac{GMm}{r}

K\rightarrow Kinetic\: energy

U\rightarrow Potential\: energy

M\rightarrow mass\: of\: planet

m\rightarrow mass\: of\: satellite

E=K+U

E=-\frac{GMm}{2r}

E=Total\: energy

 

- wherein

K=-E

U=2E

U=-2K

 

 total mechanical energy E = \frac{-GMm}{2r}

\frac{E_{A}}{E_{B}} = \frac{m_{A}}{m_{B}}*\frac{r_{B}}{r_{A}} = \frac{3}{1}*\frac{4r}{r} = 12 : 1

 

Posted by

rishi.raj

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