1)A thin rectangular magnet suspended freely has a period of oscillation of 4 seconds. If it is broken into 2 halves (each having half the original length) and one of the pieces is suspended similarly. What is the new period of oscillation?

I solved it in the following way:

Let E1 and E2 be the moment of inertia of the magnets of length L and L/2 respectively.

E1 = M(L^2)/12

E2 = (M/2)(L^2/4)/12 = E1/8

i.e. (E1/E2) = 8

Here M is the mass of the magnet.

Let T1 and T2 be the initial and final time period.

T is proportional to (E)^(1/2)

Here m is the magnetic dipole moment of the magnet. The dipole moment of the magnet doesn’t change because the magnet is cut along its perpendicular bisector.

(T1/T2) = (E1/E2)^(1/2)

(4/T2) = (8)^(1/2)

Solving I get,

T2 = sqrt(2) seconds

But the answer given in my book is 2 seconds. Please guide me.