A) the length of the day will be more than \[24\text{ }h\]
B) the length of the day will be less than \[24\text{ }h\]
C) the length of the day will remain as \[24\text{ }h\] the length of the day will become more
D) than \[24\text{ }h\] initially and then becomes equal to \[24\text{ }h\]
Correct Answer: A
Solution :
The moment of inertia of a system increases, if the mass concentrated near the axis of rotation is spread out. This is exactly what will happen, when the ice on the polar caps melts. Since no external torque acts, the angular momentum \[\text{I}\omega =constant\]. Accordingly, when moment of inertia of the earth increases due to the melting of the ice its angular speed will decrease. As a result, the time period of rotation of the earth\[\left( T=\frac{2\pi }{\omega } \right)\],ie, the duration of the day will increase.
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