A metal wire of linear mass density of 9.8 ~g / m is stretched with...

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

Options

A $50 \mathrm{~Hz}$
B $100 \mathrm{~Hz}$
C $200 \mathrm{~Hz}$
D $25 \mathrm{~Hz}$

Correct answer

A. $50 \mathrm{~Hz}$

Step-by-step 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}

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