JEE Mains · Physics · STD 11 - 7. gravitation
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
- A \( - \frac{{GMm}}{{2R}}\)
- B \( + \frac{{GMm}}{{6R}}\)
- C \( - \frac{{GMm}}{{6R}}\)
- D \( \frac{{GMm}}{{2R}}\)
Answer & Solution
Correct Answer
(C) \( - \frac{{GMm}}{{6R}}\)
Step-by-step Solution
Detailed explanation
Initial gravitational potential energy, \({E_i} = - \frac{{GMm}}{{2R}}\) Final gravitational potential energy, \({E_f} = - \frac{{GMm/2}}{{2\left( {\frac{R}{2}} \right)}}\frac{{GMm/2}}{{2\left( {\frac{{3R}}{2}} \right)}}\) \( = - \frac{{GMm}}{{2R}} - \frac{{GMm}}{{6R}}\)…
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