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

Options

A. remain same
B. remain half
C. decrease to quarter
D. increase

Explanation

To solve the problem of how the value of gravitational acceleration (g) at the equator would change if the Earth stops rotating, we can follow these steps:

### Step 1: Understand the Current Value of g
The gravitational acceleration at the surface of the Earth is given by the formula:
\[ g = G \left( \frac{M}{r^2} \right) \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( r \) is the radius of the Earth.

### Step 2: Consider the Effect of Earth's Rotation
When the Earth rotates, there is a centrifugal force acting outward at the equator due to this rotation. This force reduces the effective gravitational acceleration experienced at the equator. The effective gravitational acceleration (g') at the equator can be expressed as:
\[ g' = g - R \omega^2 \]
where:
- \( R \) is the radius of the Earth,
- \( \omega \) is the angular velocity of the Earth's rotation.

### Step 3: Analyze the Situation if the Earth Stops Rotating
If the Earth stops rotating, the centrifugal force will no longer act on objects at the equator. Therefore, the effective gravitational acceleration will no longer be reduced by the centrifugal force. This means:
\[ g' = g \]
The value of g at the equator will increase to the full gravitational acceleration value because the centrifugal force (which was reducing it) is now absent.

### Step 4: Conclusion
Thus, if the Earth stops rotating, the value of g at the equator will increase to the maximum gravitational acceleration value, which is the same as that experienced at the poles.

### Final Answer
If the Earth stops rotating, the value of g at the equator will **increase** to the maximum value of gravitational acceleration experienced on the surface of the Earth.

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