Physics-
General
Easy

Question

The length of a magnet is large compared to it's width and breadth. The time period of its oscillation in a vibration magnetometer is T. The magnet is cut along it’s length into six parts and these parts are then placed together as shown in the figure. The time period of this combination will be

  1. T    
  2. fraction numerator T over denominator square root of 3 end fraction    
  3. fraction numerator T over denominator 2 square root of 3 end fraction    
  4. Zero    

The correct answer is: fraction numerator T over denominator 2 square root of 3 end fraction


    T equals 2 pi square root of fraction numerator I over denominator M H end fraction end root; M I of each part equals fraction numerator I over denominator 6 to the power of 3 end exponent end fraction
    and magnetic moment of each part equals fraction numerator M over denominator 6 end fraction
    so net MI of system equals fraction numerator I over denominator 6 to the power of 3 end exponent end fraction cross times 6 equals fraction numerator I over denominator 6 to the power of 2 end exponent end fraction
    and net magnetic moment equals fraction numerator 4 M over denominator 6 end fraction minus fraction numerator 2 M over denominator 6 end fraction equals fraction numerator M over denominator 3 end fraction
    \ time period of the system
    T to the power of ´ end exponent equals 2 pi square root of fraction numerator I divided by 36 over denominator left parenthesis M divided by 3 right parenthesis H end fraction end root equals fraction numerator 1 over denominator 2 square root of 3 end fraction 2 pi square root of fraction numerator I over denominator M H end fraction end root equals fraction numerator T over denominator 2 square root of 3 end fraction

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