If a satellite orbiting the Earth is 9 times closer to the Earth...

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.

Options

A27 days
B1 day
C81 days
D3 days

Correct answer

B. 1 day

Step-by-step solution

\begin{aligned} & \mathrm{T}^2 \propto \mathrm{R}^3 \\ & \left(\frac{\mathrm{ T}_{\mathrm{m}}}{\mathrm{T}_{\mathrm{s}}}\right)^2=\left(\frac{\mathrm{R}}{\mathrm{R} / 9}\right)^3 \\ & \frac{\mathrm{ T}_{\mathrm{m}}}{\mathrm{T}_{\mathrm{s}}}=(3)^3 \\ & \Rightarrow \mathrm{ T}_{\mathrm{s}}=\left(\frac{27}{27}\right)=1 \text{ day }\end{aligned}

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