JEE Main 2025 Jan 23 Shift 2, Physics Q10: Satellite, Planetary Motion And Kepler’s Law

JEE Main2025Jan 23, Shift 2Physics

If a satellite orbiting the Earth is $9$ times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $= 27$ days and gravitational attraction between the satellite and the moon is neglected.

A
$1$ day
B
$81$ days
C
$27$ days
D
$3$ days

Solution

Kepler's third law: $T^{2} \propto R^{3}$ for orbits around the same central body.

With $R_{s} = \frac{R _{m}}{9}$ :

$(\frac{T _{s}}{T _{m}})^{2} = (\frac{R _{s}}{R _{m}})^{3} = (\frac{1}{9})^{3} = \frac{1}{729} .$

$\frac{T _{s}}{T _{m}} = \frac{1}{27} \Rightarrow T_{s} = \frac{27}{27} = 1$ day.

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JEE Main 2025 Jan 23 Shift 2, Physics Q10: Satellite, Planetary Motion And Kepler’s Law

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