A thin rectangular bar magnet suspended freely has period of oscillation of 4 seconds. What will be period of oscillation if the magnet is broken into two halves; each having length half of original; and one piece is made to oscillate in the same field.

2 s

Time Period of oscillating magnet is given bt $ T = 2\pi \sqrt {\frac{I}{MB}}$

Where $I = \frac{ML^2}{12}$

When the magnet is broken in two equal parts, the new magnetic dipole moment is 

Mass of broken part $M' = \frac{M}{2}$

Length of broken part $L' = \frac{L}{2}$

Moment of Inertia of broken part $I' = \frac{M'L'^2}{12}=\frac{ML^2}{96}=\frac{I}{8}$

Ratio of time Period $\frac{T'}{T} = \sqrt{\frac{I'}{M'}\times\frac{M}{I}}=\sqrt{\frac{I'}{I}\times\frac{M}{M'}}=\sqrt{\frac{1}{8}\times\frac{2}{1}} =\frac{1}{2} $

$\Rightarrow T'= 2 s$