JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Gravitation

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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✓ Correct
(B)81 days
(C)27 days
(D)3 days

Answer: (A)

Solution

By Kepler's third law,

T^{2} \propto R^{3}

for bodies orbiting the same central mass (Earth).

Let

R_{m}

be the Moon's orbital radius; the satellite's orbital radius is then

R_{m} /9

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

\frac{T _{m}}{T _{s}} = 27

T_{s} = \frac{T _{m}}{27} = \frac{27 days}{27} = 1 day

The satellite completes one revolution in

1

day.

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option

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