Solution:
By conservation of angular momentum, \(I_1 \omega_1 = I_2 \omega_2\). Since \(I \propto R^2\) and \(\omega \propto 1/T\), we get \(T_2 = T_1 \left(\frac{R_2}{R_1}\right)^2 = 24 \left(\frac{1}{\sqrt{3}}\right)^2 = 8\text{ hrs}\).
Keeping the mass of earth to be constant if its radius changes from \(R\) to \(\frac{R}{\sqrt{3}}\), then new duration of the day will be
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