c
(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 \(I' = \frac{{{\rm{w}}{l^2}}}{{12}} = \frac{{\frac{{\rm{w}}}{4}.{{\left( {\frac{1}{2}} \right)}^2}}}{{12}} = \frac{1}{{16}}.\frac{{{\rm{w}}{l^2}}}{{12}}\)
Here \(w\)  is the mass of magnet.
\(\therefore \,I' = \frac{1}{{16}}I\); Time period of each part \(T' = 2\pi \sqrt {\frac{{I'}}{{M'{B_H}}}} \)
\( = 2\pi \sqrt {\frac{{I/16}}{{(M/4){B_H}}}} = 2\pi \sqrt {\frac{I}{{4M{B_H}}}} = \frac{T}{2}\)