If the earth stops rotating about its axis, then the magnitude of gravity

Options

A. (a)increases everywhere on the surface of earth
B. (b)will increases only at the poles
C. (c)will not change at the poles
D. (d)All of the above

Explanation

To solve the problem of how gravity would change if the Earth stopped rotating about its axis, we can follow these steps:

### Step 1: Understand the effect of Earth's rotation on gravity
The effective gravitational acceleration \( G' \) at any point on the Earth's surface is given by the equation:
\[ G' = G - R \omega^2 \cos^2(\theta) \]
where:
- \( G \) is the standard gravitational acceleration (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( R \) is the radius of the Earth,
- \( \omega \) is the angular velocity of the Earth's rotation,
- \( \theta \) is the latitude angle.

### Step 2: Analyze the equation
When the Earth is rotating, the term \( R \omega^2 \cos^2(\theta) \) represents the centrifugal force effect due to rotation, which reduces the effective gravity \( G' \) at the equator (where \( \theta = 0^\circ \)) and has no effect at the poles (where \( \theta = 90^\circ \)).

### Step 3: Consider the scenario where the Earth stops rotating
If the Earth stops rotating, then \( \omega = 0 \). Substituting this into the equation gives:
\[ G' = G - R \cdot 0^2 \cdot \cos^2(\theta) = G \]
This means that the effective gravitational acceleration \( G' \) would equal the standard gravitational acceleration \( G \) everywhere on the surface of the Earth.

### Step 4: Determine the implications at different latitudes
- At the poles (\( \theta = 90^\circ \)), the centrifugal force is already zero, so \( G' \) remains \( G \).
- At the equator (\( \theta = 0^\circ \)), the centrifugal force reduces the effective gravity while the Earth is rotating. If it stops, this reduction disappears, and \( G' \) increases to \( G \).

### Conclusion
Thus, if the Earth stops rotating, the magnitude of gravity would increase at the equator and remain unchanged at the poles.

### Final Answer
The correct conclusion is that gravity will increase everywhere on the surface of the Earth, but it will not change at the poles.

---