A satellite of mass m is revolving close to t | vedclass

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(D) The time period $T$ of a satellite revolving close to the surface of a planet of radius $R$ and mass $M$ is given by $T = 2 \pi \sqrt{\frac{R^3}{G

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$\frac{3 \pi}{d T^2}$

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(D) The time period $T$ of a satellite revolving close to the surface of a planet of radius $R$ and mass $M$ is given by $T = 2 \pi \sqrt{\frac{R^3}{GM}}$.Squaring both sides,we get $T^2 = \frac{4 \pi^2 R^3}{GM}$.The mass of the planet is $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R^3 d$.Substituting the value of $M$ into the time period equation:$T^2 = \frac{4 \pi^2 R^3}{G (\frac{4}{3} \pi R^3 d)}$.Canceling $R^3$ and simplifying the expression:$T^2 = \frac{4 \pi^2}{G \cdot \frac{4}{3} \pi d} = \frac{3 \pi}{G d}$.Rearranging to solve for $G$:$G = \frac{3 \pi}{d T^2}$.

$A$ satellite of mass $m$ is revolving close to the surface of a planet of density $d$ with time period $T$. The value of the universal gravitational constant $G$ in terms of $d$ and $T$ is given by:

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