Question

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

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

Answer 1

Answer: (B)

$1.77$

As we know, frequency
$f\propto \sqrt{mg}$ or $f\propto \sqrt{g}$
In water, $f_w=0.8f_{air}$
$\frac{g^{\prime }}{f}(0.8{)}^2=0.64$
$\Rightarrow 1-\frac{{\rho }_w}{{\rho }_m}=0.64$
$\Rightarrow \frac{{\rho }_w}{{\rho }_m}=0.36....\left(1\right)$
In liquid, $\frac{g^{\prime }}{g}=(0.6{)}^2=0.36$
$1-\frac{{\rho }_1}{{\rho }_m}=0.36\frac{{\rho }_1}{{\rho }_m}=0.64.....\left(2\right)$
From eq. $\left(1\right)$ and $\left(2\right)$
$\frac{{\rho }_l}{{\rho }_n}=\frac{0.64}{0.36}\therefore {\rho }_l=1.77$.