Question

A steel rod has a radius of $10$mm and a length of $1.0$m. A force stretches it along its length and produces a strain of $0.16\%$. Young's modulus of the steel is $2.0\times {10}^{11}N/m^2$. What is the magnitude of the force stretching the rod?

• A. $100$kN
• B. $314$kN
• C. $31.4$kN
• D. $200$kN

Answer 1

Answer: (A)

$100$kN

$r=10\times {10}^{-3}m,l=1m$,
$\Delta l=\frac{0.16}{100}l$ and $Y=2\times {10}^{11}N/m^2$
$F=\frac{YA\Delta l}{l}=2\times {10}^{11}\times 3.14\times {10}^{-4}\times 0.16\times {10}^{-2}$
$=100$kN.