Question

Given below are two statements: Statement I: A satellite is moving around earth in an 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 \(R_e\) is the radius of earth and \(g\) is acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below.

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

Hint:

For satellites near the earth surface, the time period depends only on earth’s radius and acceleration due to gravity.

Answer 1

The Correct Option is D

Step 1: Analyse Statement I.
For a satellite moving very close to the earth surface, the time period is given by \[ T = 2\pi \sqrt{\frac{R_e}{g}} \] This expression depends on \(R_e\) and \(g\), not directly on the density of earth. Hence, Statement I is false.

Step 2: Analyse Statement II.
The correct expression for the time period of a satellite very close to the earth surface is \[ T = 2\pi \sqrt{\frac{R_e}{g}} \] However, the given statement incorrectly presents the dependence and context, making the statement incorrect as framed. Hence, Statement II is also false.

Step 3: Conclusion.
Both Statement I and Statement II are false.

Final Answer: \[ \boxed{\text{Both Statement I and Statement II are false}} \]