A metal wire of linear mass density of $9.8 \mathrm{~g} / \mathrm{m}$ is stretched with a tension of $10…

A metal wire of linear mass density of $9.8 \mathrm{~g} / \mathrm{m}$ is stretched with a tension of $10 \mathrm{~kg}$-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 $n$. The frequency $n$ of the alternating source is
  1. $50 \mathrm{~Hz}$
  2. $100 \mathrm{~Hz}$
  3. $200 \mathrm{~Hz}$
  4. $25 \mathrm{~Hz}$

Solution

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

Asked in: JEE Main 2003

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