The circular coil C1 has a radius of R, a length of L, and a number of turns per unit length of n1 = L/2R.
The square C2 has a side, a perimeter, and a number of turns per unit length of n2 = L/4a.
Magnetic moment of C1 = m1 = n1iA1
Magnetic moment of C2 = m2 = n2iA2
m1 = LiR/2
m2 = Lia/4
Moment of inertia of C1 = I1 = MR2/2
Moment of inertia of C2 = Ma2/12
Solving the above, we get, a = 3R