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Gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsGravitation2 Marks
Question
The radius of a planet is $R_1$ and a satellite revolves round it in a circle of radius $R_2$. The time period of revolution is $T$. Find the acceleration due to the gravitation of the planet at its surface.
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Answer

$\text{T}=2\pi\sqrt{\frac{\text{R}_2^3}{\text{gR}_1^2}}$$\text{T}^2=4\pi^2\frac{\text{R}_2^3}{\text{gR}_1^2}$
$\text{g}=\frac{4\pi^2\text{R}_2^3}{\text{T}^2\text{R}_1^2}$
$\therefore$ Acceleration due to gravity of the planet is $=\frac{4\pi^2\text{R}_2^3}{\text{T}^2\text{R}_1^2}$

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