A string is under tension of 180 N and mass per unit length $2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}$. It…

A string is under tension of 180 N and mass per unit length $2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}$. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz . The mass of the string is
  1. 1 gram
  2. 2 gram
  3. 3 gram
  4. 4 gram

Solution

$\begin{aligned} \text { Fundamental frequency } & =\mathrm{f}_2-\mathrm{f}_1 \\ & =450-375 \\ & =75 \mathrm{~Hz}\end{aligned}$ $\begin{aligned} \mathrm{f} & =\frac{1}{2 \mathrm{~L}} \sqrt{\frac{\mathrm{~T}}{\mu}} \\ 75 & =\frac{1}{2 \mathrm{~L}} \sqrt{\frac{180}{2 \times 10^{-3}}} \\ \mathrm{~L} & =2 \mathrm{~m} \\ \mu & =\frac{\mathrm{m}}{\mathrm{~L}} \\ \mathrm{~m} & =2 \times 10^{-3} \times 2 \\ & =4 \text { gram } \end{aligned}$ ...where $\mu$ is mass per unit length

Asked in: MHT CET 2024 (16 May Shift 1)

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