Question

a uniform wire of steel of 2.5m and density 8x10³ kg/m³ weighs 50x10raised to -3 when stretched by a force of 10KgF, the length increases by 2mm. calculate youngs modulus of elasticity ??

Answer 1

$$\begin{gathered} Youngsmodulusisgivenby: \\ Y=\frac{{\displaystyle \frac{Force}{area}}}{{\displaystyle \frac{changeinlength}{originallength}}} \\ Y=\frac{{\displaystyle \frac{force}{mass/(density\times length)}}}{\frac{changeinlength}{originallength}} \\ Y=\frac{force\times lengt{h}^2\times density}{mass\times chnageinlength} \\ Y=\frac{10\times 10{\left(2.5\right)}^2\times 8\times {10}^3}{50\times {10}^{-3}\times 2\times {10}^{-3}} \\ Y=5\times {10}^{8}N/m^2 \end{gathered}$$