Time period of a suspended magnet is given by T=2π√‌
l
MB
where, I= moment of inertia of the magnet about the point of suspension. M= magnetic moment B= magnetic field When the magnet is broken in length T2′=2π√‌
l′
M′B
⇒‌‌‌
T
T2′
=√‌
1
I′
×√‌
M′
M
=√‌
mL2
m′L2
×√‌
L′
L
Here, m and m ' are the masses of the magnet and L and L's are their lengths.