TS EAMCET · Physics · Gravitation
A planet of mass \(m\) moves around the Sun along an elliptical path with a period of revolution \(T\). During the motion, the planet's maximum and minimum distance from Sun is \(R\) and \(\frac{R}{3}\) respectively. If \(T^2=\alpha R^3\), then the magnitude of constant \(\alpha\) will be
- A \(\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}\)
- B \(\frac{20}{27} \cdot \frac{\pi^2}{\mathrm{Gm}}\)
- C \(\frac{32}{27} \cdot \frac{\pi^2}{\mathrm{Gm}}\)
- D \(\frac{1}{18} \cdot \frac{\pi^2}{\mathrm{Gm}}\)
Answer & Solution
Correct Answer
(C) \(\frac{32}{27} \cdot \frac{\pi^2}{\mathrm{Gm}}\)
Step-by-step Solution
Detailed explanation
Given, mass of planet \(=\mathrm{m}\) Maximum and minimum distance of the planet from Sun is \(R\) and \(\frac{R}{3}\), respectively. \(\therefore\) Semi-major axis of elliptical path of planet around the Sun, \(a=\frac{R+\frac{R}{3}}{2}=\frac{2 R}{3}\) \(\therefore\) Time…
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