GravitationHard

Question

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 $T = 2\pi\sqrt{\frac{R_{e}}{g}}$ (for satellite very close to the earth surface), where $R_{e}$ radius of earth and $g$ acceleration due to gravity.

In the light of the above statements, choose the correct answer from the options given below :

Options

A.Both Statement I and Statement II are false
B.Both Statement I and Statement II are true
C.Statement I is true but Statement II is false
D.Statement I is false but Statement II is true

Solution

$T = 2\pi\sqrt{\frac{R^{3}}{GM}}$

$${\because M = \rho \cdot \frac{4}{3}\pi R^{3} }{\therefore T = 2gp\sqrt{\frac{1}{Gp\frac{4}{3}\pi}} }$$Statement I is correct.

And $\therefore\frac{GM}{R^{2}} = g$

$$\therefore T = 2\pi\sqrt{\frac{R}{g}} $$Statement II is correct

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