Answer
(a) increase
(b) $261s$
Work Step by Step
(a) We know that $L=I\omega$ and the angular momentum of the Earth is conserved. Thus, the angular speed of the Earth decreases and hence the period of rotation or the length of the day increases as $\omega=\frac{2\pi}{T}$.
(b) We can find the required change in the length of the day as follows:
$T_f=(\frac{I_f-I_i}{I_i})T_i$
We plug in the known values to obtain:
$T_f=(\frac{(0.332)M_ER_E^2-(0.331)M_ER_E^2}{0.331M_ER_E^2})(24\times 3600s)$
$T_f=\frac{24\times 3600s}{331}$
$T_f=261s$
