The effect of rotation of the eath on the value of acceleration deu to gravity g is

Options

A. Maximum at both poles
B. Minimum at both poles
C. Maximum at equator and minimum at the poles
D. Minimum at the equator and maximum at the poles

Answer

To solve the question regarding the effect of the Earth's rotation on the value of acceleration due to gravity (g), we can break down the explanation into several steps:

### Step-by-Step Solution

1. **Understanding Gravity**:
The acceleration due to gravity (g) is the force of gravity acting on an object per unit mass. It is affected by the mass of the Earth and the distance from the center of the Earth.

2. **Effect of Earth's Rotation**:
The Earth rotates around its axis, which affects the apparent weight of objects on its surface. The rotation creates a centrifugal force that acts outward, reducing the effective weight of objects.

3. **Analyzing Forces at the Poles**:
At the poles, the radius of rotation (r) is effectively zero. Therefore, the centrifugal force acting on an object at the poles is also zero. The only force acting on an object is the gravitational force (mg), where m is the mass of the object.

\[ F_{\text{poles}} = mg \]

4. **Analyzing Forces at the Equator**:
At the equator, the radius of rotation is equal to the radius of the Earth (R). The centrifugal force can be calculated using the formula:

\[ F_{\text{centrifugal}} = m \frac{v^2}{R} = m \omega^2 R \]

where \( \omega \) is the angular velocity of the Earth. The effective gravitational force at the equator is:

\[ F_{\text{equator}} = mg - m \frac{v^2}{R} = mg - m \omega^2 R \]

5. **Comparing Forces**:
Since the centrifugal force at the equator reduces the effective gravitational force, we can conclude that:

\[ F_{\text{poles}} > F_{\text{equator}} \]

This means that the acceleration due to gravity (g) is greater at the poles than at the equator.

6. **Conclusion**:
The effect of the Earth's rotation results in maximum acceleration due to gravity at the poles and minimum acceleration due to gravity at the equator. Therefore, the correct answer to the question is that the value of acceleration due to gravity is maximum at the poles and minimum at the equator.

### Final Answer:
The acceleration due to gravity (g) is maximum at the poles and minimum at the equator due to the effect of Earth's rotation.

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