A thin rectangular magnet suspended freely has a period of oscillation equal to `T`. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is `T^(')`, then ratio `T^(')/T` is

Explanation

When magnet is divided into equal parts, the magnetic dipole moment,
`M="pole strength" xx(l)/(2)=(M)/(2)["Pole stregth remains same"]`
Also, the mass of magnet becomes half i.e. `m'=(m)/(2)`.
Moment of inertia of magnet , `I=(ml^(2)/(12))`
New moment of inertia, `I'-=(1)/(12)((m)/(2))((l)/(2))^(2)=(ml^(2))/(12xx8)`
`Rightarrow " " I'=(I)/(8)`
`Now " " T=2pi sqrt((I)/(MB))`
`and " " T'=2pi sqrt(((I)/(MB)))=2pisqrt(((I//8)/(MB//2)))`
` " " T'=(T)/(2) Rightarrow (T')/(2)=(1)/(2)`