If the earth stops rotating, the value of ‘ g ’ at the equator will

Options

A. increases
B. decreases
C. no effect
D. None of these

Explanation

To determine how the value of 'g' at the equator will change if the Earth stops rotating, we can analyze the forces acting on a person standing at the equator.

### Step-by-Step Solution:

1. **Understanding the Forces Acting on a Person at the Equator**:
- When the Earth is rotating, a person at the equator experiences two forces:
- The gravitational force acting downwards, which is \( mg \) (where \( m \) is the mass of the person and \( g \) is the acceleration due to gravity).
- The centrifugal force acting outward due to the rotation, which can be expressed as \( m \omega^2 R \) (where \( \omega \) is the angular velocity of the Earth's rotation and \( R \) is the radius of the Earth).

2. **Net Force When the Earth is Rotating**:
- The effective weight (the weight that a person feels) when the Earth is rotating is given by:
\[ W = mg - m\omega^2 R \]
- This means that the person feels lighter due to the centrifugal force acting against gravity.

3. **Situation When the Earth Stops Rotating**:
- If the Earth stops rotating, the angular velocity \( \omega \) becomes zero. Therefore, the centrifugal force \( m\omega^2 R \) also becomes zero.
- The effective weight of the person will then be:
\[ W = mg \]
- This indicates that the person will feel their full weight without any reduction due to the centrifugal force.

4. **Conclusion**:
- Since the effective weight increases when the centrifugal force is no longer acting, the value of 'g' at the equator will effectively increase to its full value \( g \) when the Earth stops rotating.
- Thus, the value of 'g' at the equator will increase.

### Final Answer:
The value of 'g' at the equator will **increase** if the Earth stops rotating.

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