Which of the following statement is correct ?

Options

A. Acceleration due to gravity increase with increasing altitude.
B. Acceleration due to gravity increase with increasing depth.
C. Acceleration due to gravity increase with increasing latitude.
D. Acceleration due to gravity is independent of the mass of the earth.

Explanation

To determine which statement about the acceleration due to gravity is correct, we need to analyze how gravity varies with height (altitude), depth, latitude, and the mass of the Earth.

### Step-by-Step Solution:

1. **Understanding Acceleration Due to Gravity (g)**:
- The acceleration due to gravity at the surface of the Earth is given by the formula:
\[ g = \frac{GM}{R^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( R \) is the radius of the Earth.

2. **Effect of Latitude on g**:
- The acceleration due to gravity at a latitude \( \phi \) is given by:
\[ g_{\phi} = g \cdot (1 - \frac{f}{2} \sin^2 \phi) \]
where \( f \) is the flattening factor of the Earth. This implies that \( g \) increases with increasing latitude because \( \sin^2 \phi \) increases as we move from the equator to the poles.

3. **Effect of Altitude on g**:
- The acceleration due to gravity at a height \( h \) above the Earth's surface is given by:
\[ g_h = \frac{GM}{(R + h)^2} \]
As \( h \) increases, \( g_h \) decreases because the denominator increases.

4. **Effect of Depth on g**:
- The acceleration due to gravity at a depth \( d \) below the Earth's surface is given by:
\[ g_d = g \cdot \left(1 - \frac{d}{R}\right) \]
As \( d \) increases, \( g_d \) decreases because the term \( (1 - \frac{d}{R}) \) becomes smaller.

5. **Mass of the Earth**:
- The acceleration due to gravity is directly proportional to the mass of the Earth. If the mass of the Earth were to change, \( g \) would change. However, the statement that "acceleration due to gravity is independent of the mass of the Earth" is incorrect.

### Summary of Findings:
- **Correct Statement**: Acceleration due to gravity increases with increasing latitude.
- **Incorrect Statements**:
- Acceleration due to gravity increases with increasing depth.
- Acceleration due to gravity increases with increasing altitude.
- Acceleration due to gravity is independent of the mass of the Earth.

### Conclusion:
The correct option is that acceleration due to gravity increases with increasing latitude.