Explanation

(b) The time period of oscillations of magnet
$T = 2\pi\sqrt{\left( \frac{I}{MB_{H}} \right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Where $I =$ moment of inertia of magnet
$= \frac{mL^{2}}{12}$ (m, being the mass of magnet)
When the three equal parts of magnet are placed on one another with their like poles together, then
$\ \ \ \ \ \ \ \ \ \ \ I^{'} = \frac{1}{12}\left( \frac{m}{3} \right) \times \left( \frac{L}{3} \right)^{2} \times 3$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{12}\frac{mL^{2}}{9} = \frac{I}{9}$
and $M^{'} =$ pole strength $\times \frac{L}{3} \times 3 = M$
Hence, $T^{'} = 2\pi\sqrt{\left( \frac{I/9}{MB_{H}} \right)}$
$\Rightarrow \ \ \ \ \ \ \ \ T^{'} = \frac{1}{3} \times T$
$\ \ \ \ \ \ \ \ \ \ \ \ \ T^{'} = \frac{2}{3}\ s$