If rho is the density of the planet,the time | vedclass

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(C) The time period $T$ of a satellite orbiting near the surface of a planet is given by $T = 2 \pi \sqrt{\frac{R^3}{GM}}$.Here,$R$ is the radius of t

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

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(C) The time period $T$ of a satellite orbiting near the surface of a planet is given by $T = 2 \pi \sqrt{\frac{R^3}{GM}}$.Here,$R$ is the radius of the planet and $M$ is its mass.The mass $M$ of the planet can be expressed in terms of its density $\rho$ as $M = \rho \cdot V = \rho \cdot \frac{4}{3} \pi R^3$.Substituting this value of $M$ into the time period formula:$T = 2 \pi \sqrt{\frac{R^3}{G \cdot (\frac{4}{3} \pi R^3 \rho)}}$$T = 2 \pi \sqrt{\frac{R^3 \cdot 3}{4 \pi G R^3 \rho}}$$T = 2 \pi \sqrt{\frac{3}{4 \pi G \rho}}$$T = \sqrt{\frac{4 \pi^2 \cdot 3}{4 \pi G \rho}}$$T = \sqrt{\frac{3 \pi}{G \rho}}$

If $\rho$ is the density of the planet,the time period of a nearby satellite is given by

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