A bar magnet of magnetic moment m and moment of inertia I is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the midpoint, perpendicular to the length, in a magnetic field B. What would be the similar period T’ for each piece?
Time period of this type of S.H.M is T=2πMBI where, I is moment of inertia M is mass of magnet. B is magnetic field According to this problem, a magnet is oscillating in a uniform magnetic field so, T=2πMBI Here, I=12ml2 when magnet is cut into two equal pieces, perpendicular to length, then moment of inertia of each piece of magnet about an axis perpendicular to the length passing through its center is, I′=2×4m(l/2)2=8I Magnetic dipole moment, M′=2M So, Time period of the oscillation is, T′=2πM′BI′=2π(M/2)BI/8=22πMBI ⟹T′=2T
