(a) Assuming the earth to be a homogeneous sphere of radius r and mass m, show that the period T of the earth’s rotation about its axis is related to its radius by T = (4πm/5L)r2, where L is the angular momentum of the earth due to its rotation.

(b) Suppose that the radius r changes by a very small amount ∆r due to some internal effect such as thermal expansion. Show that the fractional change in the period ∆T is given approximately by ∆T/T = 2∆r/r.

(c) By how many kilometers would the earth need to expand for the period to change by ¼ d/y so that leap years would no longer be necessary?