A load of mass $M\,kg$ is suspended from a steel wire of length $2\,m$ and radius $1.0\,mm$ in Searle’s apparatus experiment. The increase in length produced in the wire is $4.0\,mm.$ 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 ........ $mm$
JEE MAIN 2019, Diffcult
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In first case:
$\frac{{\frac{{mg}}{A}}}{{\left( {\frac{{\Delta {\ell _1}}}{\ell }} \right)}} = Y\,\,\,\,\, \Rightarrow \,\,\,\Delta {\ell _1} = \frac{{mg}}{{\left( {\frac{{YA}}{\ell }} \right)}}$
In second case:
$\frac{{\frac{{mg - B}}{A}}}{{\left( {\frac{{\Delta {\ell _1}}}{\ell }} \right)}} = Y\,\,\,\, \Rightarrow \,\,\Delta {\ell _2} = \frac{{mg - B}}{{\left( {\frac{{YA}}{\ell }} \right)}} = \frac{{\left( {\frac{{3mg}}{4}} \right)}}{{\left( {\frac{{YA}}{\ell }} \right)}}$
$ \Rightarrow \,\,\Delta {\ell _2} = \frac{3}{4}\Delta {\ell _1} = 3\,mm$
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