If the earth's ice caps melted, how long would a day last?

[Gold3nlily]

Homework Statement

Suppose that Earth's polar ice caps melted and the water returned to the oceans, so that the oceans were deeper by about 25.7 m. What effect would this have on Earth's rotation? Make an estimate of the resulting change in the length of the day.

Homework Equations

w=(2pi/T)
Iiwi=Ifwf
I (solid sphere)= (2/5)mR²
R (earth)= is this right? 6400e3?

The Attempt at a Solution

I like this problem, I keep getting it wrong though...

Iiwi=Ifwf
wf=(2pi/Tf)
Ti = 24 hours = 86400 sec

Ii(2pi/Ti)=If(2pi/Tf)
(2/5)mR²(2pi/Ti) = (2/5)m(R+27.7)²(2pi/Tf)
Cancel the fractions and the masses and the 2 pi:
R²(1/Ti) = (R+27.7)²(1/Tf)
(6400e3)²(1/86400) = (6400e3+27.7)²(1/Tf)
Tf= (6400e3+27.7)²(86400) / (6400e3)²
Tf= 5.52956e11seconds

86400 - 5.52956e11 = -5.52956e11 seconds (wrong)

I also tried keeping the hours:
Ii(2pi/Ti)=If(2pi/Tf)
(2/5)mR²(2pi/Ti) = (2/5)m(R+27.7)²(2pi/Tf)
Cancel the fractions and the masses and the 2 pi:
R²(1/Ti) = (R+27.7)²(1/Tf)
(6400e3)²(1/24) = (6400e3+27.7)²(1/Tf)
Tf= (6400e3+27.7)²(24) / (6400e3)²
Tf= 24.000207750449 hours

24 - 24.000207750449 = 2.0775e-4 hours (wrong)
I tried dividing this by 24 to get 8.6563e-6 hours (wrong)
I tried converting it to seconds: 2.0775e-4 hours(3600) = 0.748sec (wrong)

I only have one chance left. Does anyone know what I am doing wrong?

Thank you :D

 

[Fewmet]

It looks like you must have entered the numbers into the calculator or spreadsheet incorrectly when finding T_f. (You've also substituted 27.7 instead of 25.7 for the increase in radius.)

Consider that
(6400 x 10³+25.7)²/ (6400 x 10³)²
is just a little more than one. Multiply that quotient by 86400 cannot equal 5.52956 x 10¹¹.

Your attempt with hours and converting to seconds will worlk if you change 27.7 m to the given 25.7 m.