Q62 / 75 · JEE Main 2026 (22 January Shift 2) · Physics
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 $R_{\mathrm{e}}$ 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 :
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 $R_{\mathrm{e}}$ 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 :
- Correct answerABoth Statement I and Statement II are true
- BStatement I is false but Statement II is true
- CStatement I is true but Statement II is false
- DBoth Statement I and Statement II are false
Solution
Statement I: For a satellite very close to Earth's surface, $T = 2\pi\sqrt{\frac{R_e}{g}}$ where $g = \frac{GM}{R_e^2} = \frac{4\pi G \rho R_e}{3}$.
Substituting: $T = 2\pi\sqrt{\frac{3}{4\pi G \rho}}$.
This shows period depends on Earth's density $\rho$. Statement I is TRUE.
Statement II: Given directly as $T = 2\pi\sqrt{\frac{R_e}{g}}$, which is the standard formula.
Statement II is TRUE.
Both statements are true.
Substituting: $T = 2\pi\sqrt{\frac{3}{4\pi G \rho}}$.
This shows period depends on Earth's density $\rho$. Statement I is TRUE.
Statement II: Given directly as $T = 2\pi\sqrt{\frac{R_e}{g}}$, which is the standard formula.
Statement II is TRUE.
Both statements are true.
Hence, the correct answer is option: 'A'.