A metal wire of linear mass density 9.8 g / m is stretched with a tension of 10 kg-wt between two rigid supports 1 m 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 v . The frequency v of alternating source is

Question

A metal wire of linear mass density 9.8 g / m is stretched with a tension of 10 kg-wt between two rigid supports 1 m 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 v . The frequency v of alternating source is (A) 50 Hz (B) 100 Hz (C) 200 Hz (D) 25 Hz

Tardigrade Admin · Accepted Answer

Frequency, f=(1/2 l) √(T/ρ) =(1/2 × 1) √(10 × 9.8/9.8 × 10-3) =(1/2) √104 =(100/2) =50 H z

50 Hz

100 Hz

200 Hz

25 Hz

Frequency, f=2l1​ρT​​ =2×11​9.8×10−310×9.8​​ =21​104​ =2100​ =50Hz

Frequency, $f = \frac{1}{2 l} \frac{T}{ρ}$
$= \frac{1}{2 \times 1} \frac{10 \times 9.8}{9.8 \times 1 0 ^{- 3}}$
$= \frac{1}{2} 1 0^{4}$
$= \frac{100}{2}$
$= 50 Hz$