Gravitation

JEE Main level, single correct, medium

165 of 223

Question 165 of 223

Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is T=2πRegT=2 \pi \sqrt{\frac{R_{e}}{g}} (for satellite very close to the earth surface), where ReR_{\mathrm{e}} radius of earth and gg acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below :

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Answer: (A) Both Statement I and Statement II are true

Statement I: For a satellite very close to Earth's surface, T=2πRegT = 2\pi\sqrt{\frac{R_e}{g}} where g=GMRe2=4πGρRe3g = \frac{GM}{R_e^2} = \frac{4\pi G \rho R_e}{3}.
Substituting: T=2π34πGρT = 2\pi\sqrt{\frac{3}{4\pi G \rho}}.
This shows period depends on Earth's density ρ\rho. Statement I is TRUE.
Statement II: Given directly as T=2πRegT = 2\pi\sqrt{\frac{R_e}{g}}, which is the standard formula.
Statement II is TRUE.
Both statements are true.

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