If the earth suddenly shrinks such that its radius reduces to half of its present value, then the period of rotation of the earth reduces to

When the radius of the earth is decreased to half its initial value, the value of moment of inertia reduces to ${\left(\frac{1}{4}\right)}^{th}$ of the initial value. This causes the increase in angular speed by the same degree in order to maintain the angular momentum, $L=1\omega ,$ is constant. There fore,

$\begin{array}{l}{\omega }_2=4{\omega }_1\Rightarrow \frac{2\pi }{T_2}=4\frac{2\pi }{T_1}\Rightarrow \frac{T_2}{T_1}=\frac{1}{4}\\ T_1=24hr\Rightarrow T_2=6hr\end{array}$