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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 m

1.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 :

Answers (1)

@aravind

  Energy in   orbit = -\frac{Gm_{1}m_{2}}{2r}

Initial energy = -\frac{GMm}{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}

Posted by

Safeer PP

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