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A body of mass m is moving in a circular
orbit of radius R about a planet of mass
M. At some instant, it splits into two equal
masses. The first mass moves in a circular
orbit of radius $\frac{R}{2}$ , and the other mass, in a
circular orbit of radius $\frac{3R}{2}$ . The difference
between the final and initial total energies
is :

Option 1)
$-\frac{GMm}{2R}$

Option 2)
$+\frac{GMm}{6R}$

Option 3)
$\frac{GMm}{2R}$

Option 4)
$-\frac{GMm}{6R}$

Answers (2)

best_answer

As we learned

Graph of satellite -

$E\rightarrow Energy\: of\: satellite$

$K\rightarrow Kinetic\: energy$

$U\rightarrow Potential\: energy$

- wherein

Total Energy

$E=-\frac{GMm}{2a}=const.$

$a=semi-major\: axis$

Energy in on or bit = $\frac{Gm_{1}m_{2}}{2r}$

Initial energy = $\frac{4Mm}{2r}$

final energy = $\frac{-G(\frac{m}{2})\cdot M}{2\cdot \frac{R}{2}} - \frac{G(\frac{m}{2}).M}{2\cdot (\frac{3R}{2})} - \frac{GmM}{R}\left ( \frac{1}{2} + \frac{1}{6}\right )$

$\therefore Difference = E_{f - E_{i}}$

$=\frac{-GMm}{6R}$

Option 1)

$-\frac{GMm}{2R}$

Option 2)

$+\frac{GMm}{6R}$

Option 3)

$\frac{GMm}{2R}$

Option 4)

$-\frac{GMm}{6R}$

Posted by

Avinash

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