The radius of a planet is R $_{1}$ and a satellite revolves around it in a radius R $_{2}$ Time period of revolution is $T$ . Find the acceleration due to gravity.

\frac{4 π^{2} R_{2}^{3}}{R_{1}^{2} T^{2}}

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\frac{4 π^{2} R_{2}^{2}}{R_{1} T^{2}}

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\frac{2 π^{2} R_{2}^{3}}{R_{1} T^{2}}

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\frac{4 π^{2} R_{2}}{T^{2}}

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Solution

The correct option is A $\frac{4 π^{2} R_{2}^{3}}{R_{1}^{2} T^{2}}$
The time period of a sattelite revolving around planet of mass $M$ in radius $R_{2}$ is given as $T = 2 π R_{2}^{3 / 2} / \sqrt{G M} \Rightarrow G M = 4 π R_{2}^{3} / T^{2} - (1)$
Also acceleration due togravity of planet of mass $M$ of radius $R_{1}$ is given by $g = G M / R_{1}^{2} - (2)$
From $(1) a n d (2)$ , $g = 4 π^{2} R_{2}^{3} / R_{1}^{2} T^{2}$

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The radius of a planet is R1 and a satellite revolves around it in a radius R2 Time period of revolution is T. Find the acceleration due to gravity.

The correct option is A 4π2R32R21T2The time period of a sattelite revolving around planet of mass M in radius R2 is given as T=2πR3/22/√GM⇒GM=4πR32/T2−(1)Also acceleration due togravity of planet of mass M of radius R1 is given by g=GM/R21 −(2)From (1) and (2), g=4π2R32/R21T2

The radius of a planet is R $_{1}$ and a satellite revolves around it in a radius R $_{2}$ Time period of revolution is $T$ . Find the acceleration due to gravity.