Question

The Young’s modulus of a material is $2\times 10^{11}N/m^2$ and its elastic limit is $1\times 10^{8}N/m^2$ . For a wire of $1m$ length of this material, the maximum elongation achievable is

• A. 0.2 mm
• B. 0.3 mm
• C. 0.4 mm
• D. 0.5 mm

Answer 1

Answer: (D)

Given,
Young's modulus of material $=2\times 10^{11}N/m^2$
Elastic limit or stress $=1\times 10^{8}N/m^2$
Length of the wire $=1m$ We know that,
$Y=\frac{\text{ Stress }}{\text{ Strain }}\Rightarrow Y=\frac{\text{ Stress }}{\frac{\Delta L}{l}}$
Here, $l=$ original length of the wire
$\Delta L=$ charge in the length of the wire
$\Delta L=\frac{\text{ Stress }\times l}{Y}=\frac{1\times 10^8\times 1}{2\times 10^{11}}$
$=0.5\times 10^{-3}=0.5mm$