# A long bar magnet of time period T is cut into foue equal parts by cutting it perpendicular to both length and breadth .the time period of each part is ??

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Time period T = 2 π √ ( I / μ B_e )

I = moment of inertia

μ or M = dipole moment of bar magnet

B_e = magnetic field strength of Earth's magnetic field

I1 = m L² / 3 about the point of suspension

I2 = (m/4) (L/2)² / 3 = m L² / 48 = I1 / 16

M1 = dipole moment 1 = p * L

M2 = p / 2 * L/2 = M1 / 4

T2 / T1 = √(4/16) = 1/2

so time period of each of 4 parts is 1/2 T.

I = moment of inertia

μ or M = dipole moment of bar magnet

B_e = magnetic field strength of Earth's magnetic field

I1 = m L² / 3 about the point of suspension

I2 = (m/4) (L/2)² / 3 = m L² / 48 = I1 / 16

M1 = dipole moment 1 = p * L

M2 = p / 2 * L/2 = M1 / 4

T2 / T1 = √(4/16) = 1/2

so time period of each of 4 parts is 1/2 T.