Suppose that angular velocity of rotation of earth is increased. Then, as a consequence :

Options

A. Except at poles, weight of the object on the earth will decrease.
B. Weight of the object, everywhere on the earth, will decrease.
C. There will be no change in weight any where on the earth.
D. Weight of the object, everywhere on the earth, will decrease.

Answer

To solve the problem regarding the effect of an increase in the angular velocity of the Earth's rotation on weight, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Weight**:
- Weight (W) of an object is defined as the force exerted on it due to gravity, given by the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.

2. **Effect of Earth's Rotation on Gravity**:
- The acceleration due to gravity at a point on the surface of the Earth is affected by the Earth's rotation. The effective acceleration due to gravity \( g' \) can be expressed as:
\[ g' = g - \omega^2 R \cos^2 \lambda \]
where:
- \( g \) is the standard acceleration due to gravity,
- \( \omega \) is the angular velocity of the Earth,
- \( R \) is the radius of the Earth,
- \( \lambda \) is the latitude.

3. **Analyzing the Impact of Increased Angular Velocity**:
- If the angular velocity \( \omega \) increases, the term \( \omega^2 R \cos^2 \lambda \) also increases.
- Therefore, the effective gravity \( g' \) will decrease because it is being subtracted from \( g \):
\[ g' = g - (\text{increased term}) \]

4. **Special Case at the Poles**:
- At the poles (\( \lambda = 90^\circ \)), the cosine term becomes zero:
\[ g' = g - 0 = g \]
- This means that at the poles, the effective gravity remains unchanged regardless of the angular velocity.

5. **Conclusion on Weight**:
- Since weight is directly proportional to \( g' \):
- At the poles, weight remains constant because \( g' \) does not change.
- At other latitudes, as \( g' \) decreases due to the increase in angular velocity, the weight of the object will also decrease.

### Final Answer:
- Therefore, the correct conclusion is that **the weight of objects on Earth will decrease except at the poles, where it remains constant**.