The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $$2$$ s. The magnet is cut perpendicular to its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be

Question

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $$2$$ s. The magnet is cut perpendicular to  its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be

Infinity Learn · Accepted Answer

Initially, the time period of the $$magnetT=2=2$$$$π$$IMB     ......$$(i)For$$ each part, its moment of inertia $$=I27$$ and  magnetic moment $$=$$ $$M3$$∴ Moment of inertia of system, $$Is=I27$$ x $$3=I9Magnetic$$ moment of system,  $$Ms=M3$$ x $$3=MTime$$ period of system, $$Ts=2$$$$π$$$$IsMsB=13$$ x $$2$$$$π$$$$IMB=T3=23s$$

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