Question

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

• A. 1.42
• B. 1.77
• C. 1.82
• D. 1.21

Answer 1

The Correct Option is B

As we know, frequency 
\(f \propto \sqrt{m g} \) or\( f \propto \sqrt{g}\)  
In water, f\(_{w}=0.8 f_{\text {air }} \frac{g'}{g}(0.8)^{2}=0.64\) 
\(\Rightarrow 1-\frac{\rho_{w}}{\rho_{m}}=0.64\)
\(\Rightarrow \frac{\rho_{w}}{\rho_{m}}=0.36 ...(1) \)
In liquid, \(\frac{g'}{g}=(0.6)^{2}=0.36 \)
\(1-\frac{\rho_{1}}{\rho_{m}}=0.36 \frac{\rho_{1}}{\rho_{m}}=0.64 ...(2) \) 
From e (1) and (2) 
\(\frac{\rho_{l}}{\rho_{n}}=\frac{0.64}{0.36} \)
\(\therefore \rho_{l}=1.77\)