Concern has been expressed that warming of the atmosphere, resulting from industrial pollution, could cause the polar ice caps to melt. If the polar ice caps of the earth were to melt and the water returned to the oceans, the oceans would be made deeper by about $12.2$ m. This will effect the earth's rotation. Make an estimate of the resulting change in the length of the day, assuming that all of the earth's surface is covered with oceans. Assume that the earth (excluding the polar ice caps) is a uniform sphere with a mass of $5.98 x 10^24$ kg and a radius of $6.37 \times 10^6$ m. In addition, assume that the polar ice caps do not contribute to the rotational inertia of the earth since they are located very close to the rotation axis.
From what I found out this the final formula
$$T_\text{after} = 24h \left( 1+ \dfrac53 \dfrac{M_\text{ice}}{M_\text{earth}}\right)$$
But I keep getting the wrong answer, or if not the right one what is the right one, show how it is done it will help a lot. Thanks
Conservation of angular momentum ($L=I\omega$). Look at the moment of intertia of Earth before and after adding $12.2 \text {m}$ of water to the oceans, and consider how $\omega$ must change in order for $L$ to remain unchanged.