Explanation

(c) When magnet of length $l$ is cut into four equal parts then $m^{'} = \frac{m}{2}$ and $l^{'} = \frac{l}{2};\ \therefore M^{'} = \frac{m}{2} \times \frac{l}{2} = \frac{ml}{4} = \frac{M}{4}$
New moment of inertia $I^{'} = \frac{wl^{2}}{12} = \frac{\frac{w}{4}{.\left( \frac{1}{2} \right)}^{2}}{12} = \frac{1}{16}.\frac{wl^{2}}{12}$
Here $w$ is the mass of magnet
$\therefore I^{'} = \frac{1}{16}I;$ Time period of each part $T^{'} = 2\pi\sqrt{\frac{I'}{M^{'}B_{H}}}$
$= 2\pi\sqrt{\frac{I/16}{(M/4)B_{4}}} = 2\pi\sqrt{\frac{I}{4MB_{H}}} = \frac{T}{2}$