Question

The frequency of a sonometer wire is f. The frequency becomes f/2 when the mass producing the tension is completely immersed in water and on immersing the mass in a certain liquid, frequency become f/3. The relative density of the liquid is

• A. 1.32
• B. 1.67
• C. 1.41
• D. 1.18

Answer 1

The correct option is D 1.18

$f=\frac{1}{2l}\sqrt{\frac{Mg}{\mu }}$

$f$ $\alpha$ $\sqrt{M}$

The apparent weight due to water of density $\rho$ is $Mg-V\rho g$

$\frac{1}{2}=\sqrt{\frac{M-V{\rho }_{water}}{M}}$ and $\frac{1}{3}=\sqrt{\frac{M-V{\rho }_{liquid}}{M}}$

Solving the above two equations we get

$Relative$ $Density=\frac{{\rho }_{liquid}}{{\rho }_{water}}=\frac{32}{27}=1.18$