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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Physics
Chapter
Waves and Sound

BITSAT 2015 · Physics · Waves and Sound

The frequency of a sonometer wire is 100 Hz . When the weights...

The frequency of a sonometer wire is 100Hz100 \mathrm{ Hz}. When the weights producing the tensions are completely immersed in water, the frequency becomes 80Hz80 \mathrm{ Hz} and on immersing the weights in a certain liquid, the frequency becomes 60Hz60 \mathrm{ Hz}. The specific gravity of the liquid is

Options

  1. A1.42
  2. B1.77
  3. C1.82
  4. D1.21

Correct answer

B. 1.77

Step-by-step solution

As we know, frequency f∝mgf \propto \sqrt{m g} or f∝gf \propto \sqrt{g} In water, fw=0.8fair \mathrm{f}_{\mathrm{w}}=0.8 \mathrm{f}_{\text{air }}\mathrmg′g(0.8)2=0.64⇒1−ρwρm=0.64⇒ρwρm=0.36\begin{array}{l}\frac{\mathrmg^{\prime}}{\mathrm{g}}(0.8)^{2}=0.64 \\ \Rightarrow 1-\frac{\rho_{\mathrm{w}}}{\rho_{\mathrm{m}}}=0.64 \\ \Rightarrow \frac{\rho_{\mathrm{w}}}{\rho_{\mathrm{m}}}=0.36 \end{array}Inliquid,g′g=(0.6)2=0.361−ρ1ρm=0.36ρ1ρm=0.64Fromeq.(1)and(2)ρlρn=0.640.36∴ρl=1.77In liquid, \frac{g^{\prime}}{g}=(0.6)^{2}=0.36 1-\frac{\rho_{1}}{\rho_{\mathrm{m}}}=0.36 \frac{\rho_{1}}{\rho_{\mathrm{m}}}=0.64 From eq. (1) and (2) \frac{\rho_{l}}{\rho_{n}}=\frac{0.64}{0.36} \therefore \rho_{l}=1.77
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