Question

A load of mass $Mkg$ is suspended from a steel wire of length $2m$ and radius $1.0mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0mm$. Now the load is fully immersed in a liquid of relative density $2$. The relative density of the material of load is $8$. The new value of increase in length of the steel wire is :

• A. 4.0 mm
• B. 3.0 mm
• C. 5.0 mm
• D. zero

Answer 1

Answer: (B)

$\frac{F}{A}=y.\frac{\Delta \ell }{\ell }$
$\Delta \ell \propto F$...(1)
$T=mg$
$T=mg-f_B=mg-\frac{m}{{\rho }_b}.\rho \ell .g$
$=(1-\frac{{\rho }_{\ell }}{{\rho }_b})mg$
$=(1-\frac{2}{8})mg$
$T^{\prime }=\frac{3}{4}mg$
$From(1)$
$\frac{\Delta {\ell }^{\prime }}{\Delta \ell }=\frac{T^{\prime }}{T}=\frac{3}{4}$
$\Delta {\ell }^{\prime }=\frac{3}{4}.\Delta \ell =3mm$