Answer:
If earth were to shrink suddenly, its radius R would
decrease. The moment of inertia of earth
\[\text{I }=~\frac{2}{5}\text{M}{{\text{R}}^{\text{2}}}\]would
decrease. As no external torque is acting on earth, its angular momentum
\[\text{L}=\text{I}\omega =\text{ I}\frac{2\pi }{T}\] remains constant. As I decreases, T must decrease. Hence
the length of the day will decrease.
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