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A metal wire of linear mass density of 9.8 gm^–1 is stretched between two supports 1 m apart with a tension of 10 kg wt. The wire passes at its middle point between poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of a.c. source is

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200 Hz

100 Hz

25 Hz

50 Hz

answer is B.

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Detailed Solution

$n = \frac{1}{2 l} \sqrt{\frac{mg}{μ}} = \frac{1}{2 x 1} \sqrt{\frac{10 x 9.8}{9.8 x 10^{- 3}}} \Rightarrow n = \frac{100}{2} = 50 Hz$

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