Q140 / 160 · AP EAMCET 2018 (22 Apr Shift 2) · Physics

An object of density $2000 \mathrm{~kg}-\mathrm{m}^{-3}$ is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is $200 \mathrm{~Hz}$. If the object is immersed in water such that half of its volume is submerged, then the fundamental frequency of the transverse waves in the wire is

  • A
    200 Hz
  • Correct answer
    B
    173.2 Hz
  • C
    100 Hz
  • D
    141.4 Hz

Solution

Fundamental frequency, initially $$ n_1=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}=\frac{1}{2 l} \sqrt{\frac{V g(2000)}{\mu}} $$ Fundamental frequency, finally $$ n_2=\frac{1}{2 l} \sqrt{\frac{V g\left(2000-\frac{1000}{2}\right)}{\mu}} $$ (here we applied loss of weight due to upthrust) $$ \begin{aligned} & =\frac{1}{2 l} \sqrt{\frac{V g \times 1500}{\mu}} \\ \Rightarrow \quad \frac{n_1}{n_2} & =\sqrt{\frac{2000}{1500}}=\sqrt{\frac{4}{3}} \\ \Rightarrow \quad n_2 & =\frac{n_1 \times \sqrt{3}}{2}=100 \sqrt{3} \mathrm{~Hz}=173.2 \mathrm{~Hz} \end{aligned} $$

Hence, the correct answer is option: 'B'.

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