JEE Main 2026 — Jan 22, Shift 2 — Physics solution

JEE Main2026Jan 22, Shift 2Physics

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 $T = 2 π \frac{R _{e}}{g}$ (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 :

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

For a satellite skimming the Earth's surface: $T = 2 π \frac{R ^{3}}{GM}$ with $M = ρ \cdot \frac{4}{3} π R^{3}$ , so

$T = 2 π \frac{R ^{3}}{Gρ \cdot \frac{4}{3} π R ^{3}} = \frac{3 π}{Gρ}$ .

So $T$ depends only on the density $ρ$ of the Earth - Statement I is correct.

For Statement II: using $g = \frac{GM}{R ^{2}}$ , $T = 2 π \frac{R}{g}$ - Statement II is also correct.

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