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

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, 4 s, 2 s, 8 s, 1 s

MARKS App · 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 ′ = 1 12 m 2 l 2 2 or I ′ = I 8 Also, M ′ = M 2 ∴ T ′ = 2 π I ′ M ′ B The time of vibrations = 2 π I × 2 8 × M B = 1 2 T = 1 2 × 4 = 2 s

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