Consider the following statements.
Value of g decreases linearly with distance under surface of the earth.
Value of g decreases linearly with distance above the surface of the earth. Choose the correct option.

Options

A. Only I
B. Only II
C. I and II
D. None of the above

Answer

To solve the question regarding the statements about the value of \( g \) (acceleration due to gravity) under and above the surface of the Earth, we will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** "Value of \( g \) decreases linearly with distance under the surface of the Earth."

- When we move below the surface of the Earth, the formula for the acceleration due to gravity \( g' \) at a depth \( d \) is given by:
\[ g' = g \left(1 - \frac{d}{R}\right) \]
where:
- \( g \) is the acceleration due to gravity at the surface (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( R \) is the radius of the Earth (approximately \( 6400 \, \text{km} \)),
- \( d \) is the depth below the surface.

- This equation shows that as \( d \) increases (i.e., as we go deeper), \( g' \) decreases linearly with \( d \). Thus, Statement 1 is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** "Value of \( g \) decreases linearly with distance above the surface of the Earth."

- For heights above the Earth's surface, the formula for the acceleration due to gravity \( g' \) is given by:
\[ g' = \frac{G M}{(R + h)^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth,
- \( h \) is the height above the surface.

- This formula indicates that \( g' \) varies with the square of the distance from the center of the Earth. Therefore, as \( h \) increases, \( g' \) does not decrease linearly; it decreases according to the inverse square law. Thus, Statement 2 is **not correct**.

### Conclusion
Based on the analysis:
- Statement 1 is correct.
- Statement 2 is incorrect.

The correct option is that only Statement 1 is true.

### Final Answer
**Only Statement 1 is correct.**

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