How Much Will Day Length Increase If Polar Ice Melts 10m?

[CampyPython]

Homework Statement

If the melting of the polar ice caps were to raise the water level on the Earth by 10
m, by how much would the day be lengthened? Assume that the moment of inertia of
the ice in the polar ice caps is negligible (they are very near the axis), and assume that
the extra water spreads out uniformly over the entire surface of the Earth (that is
neglect the area of the continents compared with the area of oceans). Assume that the
earth is a sphere with uniform density

Homework Equations

Isphere = (2MR^2 ) / 5

The Attempt at a Solution

I think i found the correct answer by assuming Earth's radius 6400000 m and using angular momentum.
However we are not allowed to use angular momentum since so far we have not mentioned chapter of rotational dynamics.

 

[Simon Bridge]

Conservation of energy?
Conservation of linear momentum?

What can you use? eg. what is the context in terms of the subjects most recently taught?