A steel rod has a radius $10 \,mm$ and a length of $1.0 \,m$. A force stretches it along its length and produces a strain of $0.32 \%$. Young's modulus of the steel is $2.0 \times 10^{11} \,Nm ^{-2}$. What is the magnitude of the force stretching the rod is ........ $kN$
Medium
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(b)
$\text { Strain }=0.32 \%$
$\Rightarrow \frac{\Delta L}{L} \times 100=0.32$
$\Rightarrow \frac{\Delta L}{L}=\frac{0.32}{100}$
$A=\pi r^2=3.14 \times\left(\frac{10}{1000}\right)^2$
$Y=2 \times 10^{11} \,Nm ^2$
We know
$\frac{F L}{A Y}=\Delta L$
$F=\left(\frac{\Delta L}{L}\right) \times A \times Y$
Substituting values
$F=\frac{0.32}{100} \times 3.14 \times\left(\frac{10}{1000}\right)^2 \times 2 \times 10^{11}$
$F=201 \,kN$
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