Question

A uniform heavy rod of length $L$, weight $W$ and cross-sectional area $A$ is hanging from a fixed support. Young's modulus of the material is $Y$. Find the elongation of the rod.

• A. $\frac{WL}{AY}$
• B. $\frac{WL}{2AY}$
• C. $\frac{WL}{4AY}$
• D. $\frac{WL}{3AY}$

Answer 1

Answer: (B)

$\frac{WL}{2AY}$

$T=(L-x)\frac{W}{L};elongation=\frac{Tdx}{AY}$

$=\frac{(L-x)Wdx}{LAY};Totalelongation=\frac{W}{LAY}{\int }_0^L(L-x)dx$
$=\frac{WL}{2AY}$