Humanity collectively uses energy at the average rate of about 18 Terawatts.

(a) At that rate, after one year how long would the length of the day have increased if during that year we were able to power our activities purely by harnessing the rotational kinetic energy of the earth? (The earth has moment of inertia \(I=0.33 M R^{2}\) about the north-south polar axis.)

(b) The moment of inertia of a sphere is often given as \(I=(2 / 5) M R^{2}\). What is the primary reason why this is incorrect for the earth?