Gravitation

JEE Main level, single correct, medium

202 of 223

Question 202 of 223

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=27 days and gravitational attraction between the satellite and the moon is neglected.

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Answer: (B) 1 day

T2∝R3( TmTs)2=(RR/9)3 TmTs=(3)3⇒ Ts=(2727)=1 day \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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