Question

A uniform steel bar of cross-sectional area A and length L. is suspended so that it hangs vertically. The stress at the middle point of the bar is ( $\rho$ is the density of steel)

• A. $\frac{L}{2A}\rho g$
• B. $\frac{L\rho g}{2}$
• C. $\frac{LA}{\rho g}$
• D. $L\rho g$

Answer 1

Answer: (B)

$\frac{L\rho g}{2}$

$\begin{array}{cc}\text{mass}& =\text{density}\times \text{volume.}\\ & =\frac{\rho AL}{2}\\ \text{stress}& =\frac{F}{A}=\frac{mg}{A}\end{array}$

$\begin{array}{c}=\frac{\rho ALg}{2A}\\ =\frac{\rho Lg}{2}\end{array}$