Statement I: For a satellite revolving very near to the earth's surface the time period of revolution is given by `1 h 24` min.
Statement II: The period of revolution of a satellite depends only upon its height above the earth's surface.

Options

A. Statement I is True, Statement II is True: Statement II is a correct explanation for Statement I.
B. Statement I is True, Statement II is True: Statement II is Not a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To solve the question, we need to analyze both statements provided.

### Step 1: Analyze Statement I
Statement I claims that for a satellite revolving very near to the Earth's surface, the time period of revolution is given by 1 hour and 24 minutes.

1. **Understanding the Time Period Formula**: The time period \( T \) of a satellite in orbit near the Earth can be calculated using the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where \( r \) is the radius of the orbit, \( G \) is the gravitational constant, and \( M \) is the mass of the Earth.

2. **For a satellite very near to the Earth's surface**: The radius \( r \) can be approximated as the radius of the Earth \( R \) (approximately \( 6.4 \times 10^6 \) m). The gravitational acceleration \( g \) at the surface of the Earth is approximately \( 9.81 \, \text{m/s}^2 \).

3. **Using the simplified formula**: For satellites very close to the Earth's surface, we can simplify the time period formula to:
\[ T = 2\pi \sqrt{\frac{R}{g}} \]

4. **Calculating the Time Period**:
\[ T = 2\pi \sqrt{\frac{6.4 \times 10^6 \, \text{m}}{9.81 \, \text{m/s}^2}} \approx 2\pi \sqrt{651,000} \approx 2\pi \times 807.5 \approx 5065 \, \text{s} \approx 84 \, \text{min} \]
This means that the time period is approximately 84 minutes, which is equivalent to 1 hour and 24 minutes.

### Conclusion for Statement I:
Statement I is **true**.

### Step 2: Analyze Statement II
Statement II states that the period of revolution of a satellite depends only upon its height above the Earth's surface.

1. **Understanding the Dependency**: The time period \( T \) of a satellite indeed depends on the radius of the orbit, which is directly related to the height above the Earth's surface. The formula shows that \( T \) is influenced by the gravitational pull at that height.

2. **Height and Time Period Relation**: As the height increases, the gravitational pull decreases, thus affecting the time period. However, it is important to note that the time period also depends on the mass of the Earth and the gravitational constant, which are constants.

### Conclusion for Statement II:
Statement II is **true** and correctly explains the relationship in Statement I.

### Final Conclusion:
Both statements are true, and Statement II is the correct explanation for Statement I.

### Answer:
Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I.

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