A wire of length L and mass per unit length 6.0 10^ -3 ; kgm^ -1 … - Vidyadip

MCQ

A wire of length $L$ and mass per unit length $6.0\times 10^{-3}\; \mathrm{kgm}^{-1}$ is put under tension of $540\; \mathrm{N}$. Two consecutive frequencies that it resonates at are : $420\; \mathrm{Hz}$ and $490 \;\mathrm{Hz}$. Then $\mathrm{L}$ in meters is

A
$8.1 \;m$
B
$5.1 \;m$
C
$1.1 \;m$
✓
$2.1 \;m$

✓

Answer

Correct option: D.

$2.1 \;m$

d
$\frac{\mathrm{nv}}{2 \ell}=420$

$\frac{(\mathrm{n}+1) \mathrm{v}}{2 \ell}=490$

$\frac{v}{2 \ell}=70$

$\ell=\frac{\mathrm{v}}{140}=\frac{1}{140} \sqrt{\frac{540}{6 \times 10^{-3}}}=\frac{1}{140} \sqrt{90 \times 10^{3}}$

$\ell=\frac{300}{140}=2.142$

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