The angular momentum of the earth about its axis will remain constant

$\mathrm{L}=\mathrm{I}\mathrm{\omega }=\left(\frac{2}{5}\mathrm{M}{\mathrm{R}}^2\right)\left(\frac{2\mathrm{\pi }}{\mathrm{T}}\right)$

$\Rightarrow \mathrm{T}=\frac{4\mathrm{\pi M}}{5\mathrm{L}}{\mathrm{R}}^2$

$\therefore \mathrm{T}\propto {\mathrm{R}}^2$

If the radius of earth is reduced to half of its present value then time period will become one-fourth of present value