JEE Mains · Physics · STD 11 - 7. gravitation
What is the minimum energy required to launch a satellite of mass \(m\) from the surface of a planet of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\)?
- A \(\frac{{GmM}}{{3R}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\)
- B \(\;\frac{{5GmM}}{{6R}}\)
- C \(\;\frac{{2GmM}}{{3R}}\)
- D \(\;\frac{{GmM}}{{2R}}\)
Answer & Solution
Correct Answer
(B) \(\;\frac{{5GmM}}{{6R}}\)
Step-by-step Solution
Detailed explanation
Applying energy conservation \(k + \left( { - \frac{{GMm}}{R}} \right) = \frac{1}{2}mv_0^2 + \left( { - \frac{{GMm}}{{R + h}}} \right)\) \(k - \frac{{GMm}}{R} = \frac{1}{2}m\left( {\frac{{Gm}}{{R + 2R}}} \right) - \frac{{GMm}}{{R + 2R}}\) \(\therefore k = \frac{{5GMm}}{{6R}}\)
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