By considering earth to be non spherical.
STATEMENT -1 : As one moves from equator to the pole of earth, the value of acceleration due to gravity increases.
and
STATEMENT -2 : If earth stops rotating about its own axis, the value of acceleration due to gravity will be same at pole and at equator.

Options

A. Statement 1- True, Statement -2 is True, Statement -2 is a correct explanation for Statement -1
B. Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1
C. Statement -1 is True, Statement -2 is False
D. Statement -1 is False, Statement -2 is True

Answer

To solve the problem, we need to analyze both statements regarding the acceleration due to gravity as one moves from the equator to the poles of the Earth and the effects of Earth's rotation.

### Step-by-Step Solution:

1. **Understanding Acceleration Due to Gravity (g)**:
The acceleration due to gravity at any point on the Earth's surface can be expressed as:
\[ g' = g - R \omega^2 \cos^2(\theta) \]
where:
- \( g' \) is the effective acceleration due to gravity at latitude \( \theta \),
- \( g \) is the standard acceleration due to gravity at the equator,
- \( R \) is the radius of the Earth,
- \( \omega \) is the angular velocity of the Earth,
- \( \theta \) is the latitude (0° at the equator and 90° at the poles).

2. **Analyzing Statement 1**:
As one moves from the equator (where \( \theta = 0° \)) to the poles (where \( \theta = 90° \)):
- At the equator, \( \cos^2(0°) = 1 \), so:
\[ g' = g - R \omega^2 \]
- At the poles, \( \cos^2(90°) = 0 \), so:
\[ g' = g \]
- Therefore, as you move from the equator to the poles, the centrifugal force due to Earth's rotation decreases, leading to an increase in the effective value of \( g' \). Thus, **Statement 1 is correct**.

3. **Analyzing Statement 2**:
If the Earth stops rotating, the centrifugal force disappears. The effective acceleration due to gravity at the equator would then be:
\[ g' = g \]
At the poles, it remains:
\[ g' = g \]
Hence, if the Earth stops rotating, the value of acceleration due to gravity would be the same at both the pole and the equator. Therefore, **Statement 2 is incorrect**.

4. **Conclusion**:
- Statement 1 is true: As one moves from the equator to the pole, the value of acceleration due to gravity increases.
- Statement 2 is false: If Earth stops rotating, the value of acceleration due to gravity will be the same at the pole and at the equator.

### Final Answer:
- Statement 1 is true.
- Statement 2 is false.