Question

Assertion :To increase the length of a thin steel wire of $0.1{cm}^2$ cross sectional area by $0.1$%, a force of $2000N$ is required, its $Y=200\times {10}^{9}N$ $m^{-2}$ Reason: It is calculated by $Y=\frac{F\times L}{A\times \Delta L}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\Delta L=\frac{PL}{AY}$

$\Rightarrow Y=\frac{PL}{A\left(\Delta L\right)}$

For $P=2000N$, $\frac{L}{\Delta L}=\frac{1}{0.1}$% $=1000$

$A=0.1{cm}^2$

$={10}^{-5}{m}^2$

$Y=\frac{2\times {10}^{3}N\times {10}^3}{{10}^{-5}{m}^2}=200\times {10}^{9}N/m^2$

where, $Y$ is Youngi Modulus of Elasticity.