If the density of moon is $d$ , the time period of revolution of an artificial satellite in a circular orbit very close to the surface of the moon is:

\sqrt{\frac{3 π}{16 d G}}

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\sqrt{\frac{16 π}{3 d G}}

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\sqrt{\frac{9 π}{d G}}

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\sqrt{\frac{3 π}{d G}}

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Solution

The correct option is D $\sqrt{\frac{3 π}{d G}}$
$T^{2} = \frac{4 π^{2} R^{3}}{G M} T^{2} = \frac{3 π}{G ⎡ ⎢ ⎢ ⎢ ⎣ \frac{M}{\frac{4}{3} {π R}^{3}} ⎤ ⎥ ⎥ ⎥ ⎦} = \frac{3 π}{G d} ∴ T = \sqrt{\frac{3 π}{d G}}$

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