A satellite is revolving very close to a plan | vedclass

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(C) The period of revolution $T$ of a satellite at a distance $r = R_p + h$ from the center of a planet of mass $M_p$ is given by $T = 2 \pi \sqrt{\fr

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$\sqrt{\frac{3 \pi}{\rho G}}$

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(C) The period of revolution $T$ of a satellite at a distance $r = R_p + h$ from the center of a planet of mass $M_p$ is given by $T = 2 \pi \sqrt{\frac{r^3}{G M_p}}$.Since the satellite is revolving very close to the planet,$h \approx 0$,so $r \approx R_p$.The mass of the planet in terms of its density $\rho$ and radius $R_p$ is $M_p = \frac{4}{3} \pi R_p^3 \rho$.Substituting $M_p$ into the period formula:$T = 2 \pi \sqrt{\frac{R_p^3}{G (\frac{4}{3} \pi R_p^3 \rho)}}$.Simplifying the expression:$T = 2 \pi \sqrt{\frac{3}{4 \pi G \rho}} = \sqrt{\frac{4 \pi^2 \cdot 3}{4 \pi G \rho}} = \sqrt{\frac{3 \pi}{G \rho}}$.

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

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