Questions

A spherical planet has uniform density $\frac{π}{2} \times 10^{4} kg / m^{3}$ . Find out the minimum period for a satellite in a circular orbit around it in seconds. $(Use G = \frac{20}{3} \times 10^{- 11} \frac{N - m^{2}}{{kg}^{2}}) .$

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detailed solution

Correct option is B

Time period is minimum for the satellites with minimum radius of the orbit i.e. equal to the radius of the planet. Therefore.GMmR2=mv2R⇒V=GMRTmin=2πRGMR=2πRRGM using M=43pR3⋅ρ Tmin=3πGρ Using values Tmin=3000s

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