If spining speed of the earth is decreased , then weight of the body at the poles

Options

A. Does not change
B. Decreases
C. Increases
D. May increases or decreases

Answer

To determine how the weight of a body at the poles changes if the spinning speed of the Earth is decreased, we need to analyze the effect of Earth's rotation on the acceleration due to gravity.

### Step-by-Step Solution:

1. **Understanding Weight and Gravity**:
The weight \( W \) of a body is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Acceleration Due to Gravity**:
The effective acceleration due to gravity \( g' \) at any point on Earth can be expressed as:
\[ g' = g - R \omega^2 \cos^2 \theta \]
where \( R \) is the radius of the Earth, \( \omega \) is the angular velocity of the Earth's rotation, and \( \theta \) is the angle of latitude.

3. **Analyzing at the Poles**:
At the poles, the angle of latitude \( \theta \) is \( 90^\circ \). Therefore, we have:
\[ \cos(90^\circ) = 0 \]
Substituting this into the equation for \( g' \):
\[ g' = g - R \omega^2 \cdot 0 = g \]
This means that at the poles, the effective acceleration due to gravity \( g' \) is equal to the standard acceleration due to gravity \( g \).

4. **Effect of Decreasing Spinning Speed**:
Since \( g' \) at the poles is independent of \( \omega \) (the angular speed), decreasing the spinning speed of the Earth does not affect the value of \( g' \) at the poles. Thus, the weight of a body at the poles remains the same.

5. **Conclusion**:
Therefore, if the spinning speed of the Earth is decreased, the weight of a body at the poles will remain unchanged.

### Final Answer:
The weight of the body at the poles will remain the same if the spinning speed of the Earth is decreased.

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