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Q.
What will be the percentage increase in the length of wire, if longitudinal stress of $1\,kg/mm^{2}$ is applied on it? $\left(Y = 10^{11} N / m^{2}\right)$
NTA AbhyasNTA Abhyas 2022
Solution:
from hooke's law
Stress $\propto$ Strain
From the question given that stress $=1\,kg/mm^{2}$
$\Rightarrow 1\,kg/10^{- 6}m^{2}$
$\Rightarrow 10^{6}kg/m^{2}$
Young's modulus $Y=10^{11}N/m^{2}$
$\frac{\Delta L}{L}\times 100=?$
Stress $=10^{6}\times 9.8\,N/m^{2}$
$\left[\because \frac{1 k g}{m} = 1 \times 9 . 8 \,N / m^{2}\right]$
$\Rightarrow $ Strain $=\frac{\text{Stress}}{Y}$
strain is change in length upon orignal length
$\frac{\Delta L}{L}\Rightarrow \frac{9 . 8 \times 10^{6}}{10^{11}}$
$\Rightarrow \frac{\Delta L}{L}\times 100=9.8\times 10^{- 5}\times 100$
$\Rightarrow 10\times 10^{- 5}\times 100$
$\Rightarrow 10^{- 2}$
$\left[\because 9 . 8 \simeq 10\right]$
$\frac{\Delta L}{L}\times 100=0.01$