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Home / Doubts and Solutions/JEE/Physics

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Asked by rbhatt16 18th July 2018, 12:22 PM
Answered by Expert
Answer:
period of oscillation begin mathsize 12px style T space equals space 2 pi square root of fraction numerator I over denominator M space B subscript H end fraction end root space end style , where I is moment of inertia, M is magenetic moment, BH is magnetic field induction.
 
Magenetic moment = m×2l  where m is pole strength and l is semi-length of the magnet. Since the magent is cut into three equal pieces and put toether as their like poles are same side, the pole strength is tripled but length is reduced to one-third of its original length. hence the effective magnetic moment remains same.
 
Moment of inertia I = mass ×( L2 /12 ), where L is length of magnet. (Length is much greater than its width and breadth, hence it is considered as rod )
 
After cutting the magnets into three equal parts, new moment of inertia, I' = (1/9) × mass × (L2 / 12 ) = (1/9)×I
 
Hence after cutting the magnet into three equal pieces and putting together so that their like-poles are at same side, Magnetic moment remains same and Moment of inertia is reduced by (1/9)th of its original value.  Since Moment of inertia is inside square root, the period decreases by 1/3 of its original value.
 
Hence new period = (2/3)s
Answered by Expert 18th July 2018, 1:08 PM
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