A thin magnetic needle vibrates in the horizontal plane with a period of 4 s . The needle is cut into two halves by a plane normal to the magnetic axis of the needle. Then, the period of vibration of

Question

A thin magnetic needle vibrates in the horizontal plane with a period of 4 s . The needle is cut into two halves by a plane normal to the magnetic axis of the needle. Then, the period of vibration of each half needle is approximately

TestHub · Accepted Answer

The moment of inertia of needle when it cuts into two halves by a plane normal to magnetic axis of the needle

$I^{'} = \frac{1}{12} (\frac{m}{2}) {(\frac{l}{2})}^{2}$ or $I' = \frac{I}{8}$

Also, $M' = \frac{M}{2}$

$∴ T^{'} = 2 π \sqrt{\frac{I^{'}}{M^{'} B}}$

The time of vibrations

$= 2 π \sqrt{\frac{I \times 2}{8 \times M B}}$

$= \frac{1}{2} T = \frac{1}{2} \times 4$

$= 2 s$

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