On meltng of ice on the pole of the earth, its moment of inertia will :-

Options

A. increase
B. decrease
C. remain unchanged
D. none of these

Answer

To solve the problem of how the moment of inertia of the Earth changes when ice melts at the poles and flows toward the equator, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
The moment of inertia (I) of a body is a measure of how difficult it is to change its rotational motion about an axis. It depends on the mass distribution relative to the axis of rotation.

2. **Initial Situation**:
Initially, the ice is located at the poles of the Earth. The moment of inertia of the Earth can be represented as:
\[ I_{\text{initial}} = I_{\text{Earth}} + I_{\text{ice at poles}} \]
Here, \(I_{\text{Earth}}\) is the moment of inertia of the Earth without the ice, and \(I_{\text{ice at poles}}\) is the moment of inertia contributed by the ice at the poles.

3. **Melting of Ice**:
When the ice melts, it turns into water and flows toward the equator. This means that the mass of the ice is now distributed further from the axis of rotation (the equatorial axis).

4. **Effect on Moment of Inertia**:
The moment of inertia of a mass \(m\) at a distance \(r\) from the axis of rotation is given by:
\[ I = m r^2 \]
As the water moves from the poles (where \(r\) is small) to the equator (where \(r\) is larger), the moment of inertia increases because \(r\) increases.

5. **Conservation of Angular Momentum**:
The angular momentum \(L\) of the Earth is conserved, which means:
\[ L = I \omega = \text{constant} \]
If the moment of inertia \(I\) increases due to the melting ice, the angular velocity \(\omega\) must decrease to keep the angular momentum constant.

6. **Conclusion**:
Since the moment of inertia increases when the ice melts and flows toward the equator, we conclude that the moment of inertia of the Earth increases as a result of the melting ice at the poles.

### Final Answer:
The moment of inertia of the Earth will **increase** when ice melts at the poles.

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