If the polar ice caps of the earth were to melt, what would the effect of the length of the day?

QUESTION:

If the polar ice caps of the earth were to melt, what would the effect of the length of the day be?

ANSWER:

Earth rotates about its axis passing through north and south poles of the earth (polar axis). When ice of polar caps of earth melts, mass concentrated near the axis of rotation spreads and will move away from the axis of rotation. So radius of gyration of earth (k)increases. Therefore, moment of inertia I increase.(Moment of inertia proportional to the square of the radius of gyration)

As no external torque acts, angular momentum constant.

i.e L = Iω = I(2π/T) (from this equation, we can conclude that I proportional to T)

With increase of I, T will increase i.e. length of the day will increase.

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