A : If angular speed of the earth increases , the effective g will decrease at all places on earth .
R: The value of 'g ' at latitude `lambda` is given by ` g ' = g - omega^(2)Rcos^(2)lambda`

Options

A. If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)
C. If Assertion is true statement but Reason is false , then mark (3)
D. If Assertion is false statement but Reason is true then, mark (4)

Answer

To solve the problem, we need to analyze the assertion and reason provided regarding the effect of the Earth's angular speed on the effective acceleration due to gravity (g') at different latitudes.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if the angular speed of the Earth increases, the effective g will decrease at all places on Earth.
- We need to evaluate whether this statement is true or false.

2. **Understanding the Reason**:
- The reason provided is that the value of 'g' at latitude λ is given by the formula:
\[ g' = g - R \omega^2 \cos^2 \lambda \]
- Here, \( g \) is the standard acceleration due to gravity, \( R \) is the radius of the Earth, \( \omega \) is the angular speed of the Earth, and \( \lambda \) is the latitude.

3. **Analyzing the Formula**:
- The formula indicates that the effective gravity \( g' \) decreases as the angular speed \( \omega \) increases, but this decrease is also dependent on the latitude \( \lambda \).
- Specifically, at the poles (\( \lambda = 90^\circ \)), \( \cos^2 90^\circ = 0 \), which means:
\[ g' = g - R \omega^2 \cdot 0 = g \]
- Therefore, at the poles, the effective gravity remains equal to \( g \) regardless of the angular speed.

4. **Conclusion on Assertion**:
- Since the effective gravity does not decrease at the poles (it remains constant at \( g \)), the assertion that effective g decreases at all places on Earth is incorrect.
- Thus, the assertion is **false**.

5. **Conclusion on Reason**:
- The reason provided is true as it correctly describes how the effective gravity varies with latitude and angular speed.
- Therefore, the reason is **true**.

6. **Final Evaluation**:
- Since the assertion is false and the reason is true, the correct conclusion is that the assertion is incorrect while the reason is correct.

### Final Answer:
The correct option is **Option 4**: The assertion is false, but the reason is true.