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Question:
what will be the change in the time period if the polar ice caps melt
Answer:

To a first-order effect, there would be no change.

But one consequence of melting is that the water moves to other places. Water that moves from the poles to other areas on the surface of the earth would serve to (slightly) increase the moment of inertia of the planet. This is because the mass of the water would be farther from the rotational axis. The result of this would be a slight slowing of the earths rotation compared to the situation where the ice remains intact.

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