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.
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