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Magnetism And Matter

Question
CBSEENPH12039727

The length of a magnet is large compared to its width and breadth. The time period of its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along 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

  • 2 s

  • 2/3 s

  • 2√3 s

  • 2/√3 s

Solution

B.

2/3 s

The time period of oscillations of magnet
straight T space equals space 2 space straight pi square root of open parentheses 1 over MH close parentheses end root space...... space left parenthesis straight i right parenthesis
where I = moment of inertia of magnet = mL2/12  (m is being the mass of magnet)
M = pole strength × L When the three equal parts of magnet are placed on one another with their like poles together, then
straight I apostrophe space space equals space 1 over 12 open parentheses straight m over 3 close parentheses open parentheses straight L over 3 close parentheses squared space straight x space 3
space equals space 1 over 12 mL squared over 9
space equals space straight l over 9
and space straight M apostrophe space equals space pole space strength space straight x space straight L over 3 space straight x space 3
space equals space straight M
Hence comma space straight T apostrophe space equals space 2 straight pi square root of open parentheses fraction numerator straight I divided by 9 over denominator MH end fraction close parentheses end root
straight T apostrophe space equals space 1 third space straight x space straight T
straight T space equals space 2 divided by 3 space sec