Question

On applying a stress of $20 \times 10^{8} \,Nm ^{-2}$, the length of a perfectly elastic wire is doubled. Its Young's modulus will be

• A. $40 \times 10^{8} \,Nm ^{-2}$
• B. $20 \times 10^{8} \,Nm ^{-2}$
• C. $10 \times 10^{8} \,Nm ^{-2}$
• D. $5 \times 10^{8} \,Nm ^{-2}$

Answer 1

Answer: (B)

Given, stress $F=20 \times 10^{8} \,Nm ^{-2}$
Young's modulus $=\frac{\text { Stress }}{\text { Strain }}$
As the length of wire gets doubled, therefore strain $=1$
$ {\left[\because \text { strain }=\frac{\text { change in length }}{\text { original length }}=\frac{2 L-L}{L}=1\right]} $
$\therefore Y=\text { stress }=20 \times 10^{8} \,Nm ^{-2}$