Alternating Current

JEE Main level, single correct, medium

51 of 190

Question 51 of 190

A metal wire of linear mass density of 9.8 g/m9.8 \mathrm{~g} / \mathrm{m} is stretched with a tension of 10 kg10 \mathrm{~kg}-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency nn. The frequency nn of the alternating source is

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Answer: (A) 50 Hz50 \mathrm{~Hz}

n=12lTμ;I=1mn=\frac{1}{2 l} \sqrt{\frac{T}{\mu}} ; \quad I=1 m
T=10Kg\mathrm{T}=10 \mathrm{Kg} wt. =10×10=100 N=10 \times 10=100 \mathrm{~N}
μ=9.8 g/m=9.8×10−3 kg/mn=50hz\mu=9.8 \mathrm{~g} / \mathrm{m}=9.8 \times 10^{-3} \mathrm{~kg} / \mathrm{m} \quad \mathrm{n}=50 \mathrm{hz}

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