Question

A uniform steel rod of cross-sectional area $A$ and length $L$ is suspended so that it hangs vertically. The stress at the middle point of the rod is :

• A. $\frac{1}{2}\rho gL$
• B. $\frac{1}{4}\rho gL$
• C. $\rho gL$
• D. None of these

Answer 1

The correct option is A $\frac{1}{2}\rho gL$

Force acting at the mid point of the rod is
$T=\frac{M}{2}\left(g\right)=\frac{\rho SL}{2}\left(g\right)$
$\therefore \sigma =\frac{T}{S}=\frac{1}{2}\rho gl$
Option A.