Question

A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed. support. If Young's modulus for rod is $Y$, then elongation produced in rod is

• A. $\frac{W L}{Y A}$
• B. $\frac{W L}{2 Y A}$
• C. $\frac{W L}{4 Y A}$
• D. $\frac{3 W L}{4 Y A}$

Answer 1

Answer: (B)

Center of mass is at $\frac{L}{2}$ distance from top so it can be assumed for easy calculation that $W$ weight is hanged to a $\frac{L}{2}$ length string
Now use $\frac{F L}{A Y} \cdot \Delta L$
$\Delta L=\frac{W \times L}{2 A Y}$