Length of the day change if polar ice caps melt.

[Jomaho]

Homework Statement

Question requires assumption that the Earth is spherical, all the ice is located at the axis of rotation.
Basically if all the ice was to melt uniformally over the surface of the earth, what would be the change in the length of the day?
Mass of ice: m= 2.3*10^19 kg
Mass of earth: M= 6.4*10^24 kg (doesn't say whether this takes into account the ice, I assumed it does)

Homework Equations

Moment of inertia of a solid sphere: I=2m(r^2)/5
Moment of inertia of a spherical shell I=2m(r^2)/3
m=mass
r=radius

The Attempt at a Solution

I went about it as follows:

Initially: I₁=2M(r^2)/5
After: I₂=2(M-m)(r^2)/5 + 2m(r^2)/3

I then used conservation of momentum:
L= I₁w₁ = I₂w₂

Finally using:
Time diff = 2*pi*((1/w₂)-(1/w₁))
Where 2*pi/w₁ = 24hours

This eventually canceled down to:
Time diff = (4*pi*m)/(3*w₁*M)

I got the answer to be 0.621s. Would someone mind checking my method and answer?

 

[Jomaho]

Scratch that end answer, I've got 0.207s. Must not have divided by 3.