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Satellites - Orbital Velocity & Period question from NEET 2019

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Satellites - Orbital Velocity & Period

The time period of a geostationary satellite is 24 h, at a height $6R_E$ ( $R_E$ is radius of earth) from surface of earth. The time period of another satellite whose height is $2.5\,R_E$ from surface will be,

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Answer: (b)

Orbit radii: $r_1 = 7R_E$ ( $T_1 = 24$ h), $r_2 = 3.5R_E$ .
$T_2 = 24\left(\frac{3.5}{7}\right)^{3/2} = \frac{24}{2\sqrt{2}}$
$T_2 = 6\sqrt{2}$ h
So the answer is (b).

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