question_answer

A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is \[2\times {{10}^{11}}N{{m}^{-2}}.\] The percentage strain is about [JEE ONLINE 07-05-2012]

A)  0.16%          

B)       0.32% C)  0.08%              D)       0.24% Correct Answer: A Solution : [a] Given: \[F=100kN={{10}^{5}}N\]

\[Y=2\times {{10}^{11}}N{{m}^{-2}}\]

\[{{\ell }_{0}}=1.0m\]

radius r = 10 mm= 10-2m

From formula, \[\text{Y=}\frac{\text{Stress}}{\text{Strain}}\]

\[\Rightarrow \]Strain \[\text{=}\frac{\text{Stress}}{Y}=\frac{S}{AY}\]

\[\text{=}\frac{{{10}^{5}}}{\pi {{r}^{2}}Y}=\frac{{{10}^{5}}}{3.14\times {{10}^{-4}}\times 2\times {{10}^{11}}}\]

\[=\frac{1}{628}\]

Therefore % strain \[=\frac{1}{628}\times 100=0.16%\]