Effect on length of day as the polar ice caps melt If the polar ice caps of the Earth melt, how will the length of the day be affected?
 A: The short answer is about less than a second.
You can do a quick-and-dirty calculation by assuming that the mass of the polar ice caps (roughly $10^{19}$ kg or about $\frac{1}{200,000}$ of earth's mass). We expect then that this would slow earth's rotation by that same amount (because the mass flows from the poles to the equator):
$$
\frac{1}{200,000}\cdot86000\,{\rm s}\approx0.43\,{\rm s}
$$
You can do a more complicated solution involving rotational kinetic energy, $K=\frac12I\omega^2$, but this will not change the answer significantly (increases it to something like 2/3 a second) than the quick and dirty solution.
A: The polar ice will melt, due to increase of temperature in earth's surface, by global warming. The rate of cooling of earth's inner heat will be slow, resulting more molten lava in the lower mantle, will be changed into liquid. The heavier mass of the liquid will go down, resulting decrease of angular momentum.
Conclusion-Increase of angular momentum of water(ice), may be neutralized by decrease in the angular momentum in the liquid outer core of earth.  
A: the duration of the day will be slightly changed because when polar caps of earth melt then the mass of the earth and the radius will also decrease significantly will cause to decrease the time period also.
i.e. T=2π√R/GM 
A: If no external torque is applied then You should know that in a system Ik is constant[I=rotational inertia k=angular velocity] if ice from pole melts then surely mass distribution will be affected and I will be change(i left to you to find wether it increase or decreasf)  so k will changed[since Ik = constant]there for k ie velocity of rotation will change so length of day ie time taken for rotation will also change
