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

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 $T = 2 π \sqrt{\frac{R_{e}}{g}}$ (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 : [2026]

Smart Achievers · Accepted Answer

(3)

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$

$∵$ $M = ρ \cdot \frac{4}{3} π R^{3}$

$∴$ $T = 2 g p \sqrt{\frac{1}{G ρ \frac{4}{3} π}}$

$Statement I is correct.$

$And$ $∴$ $\frac{G M}{R^{2}} = g$

$∴$ $T = 2 π \sqrt{\frac{R}{g}}$

$Statement II is correct$

$Ans. (3)$

Solution

1 Statement I is true but Statement II is false

2 Statement I is false but Statement II is true

3 Both Statement I and Statement II are true

4 Both Statement I and Statement II are false

Ans.
(3)

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$

$∵$ $M = ρ \cdot \frac{4}{3} π R^{3}$

$∴$ $T = 2 g p \sqrt{\frac{1}{G ρ \frac{4}{3} π}}$

$Statement I is correct.$

$And$ $∴$ $\frac{G M}{R^{2}} = g$

$∴$ $T = 2 π \sqrt{\frac{R}{g}}$

$Statement II is correct$

$Ans. (3)$

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