Question

One end of uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $s$ is the area of cross-section of the wire, the stress in the wire at a height $\left(L/4\right)$ from its lower end is

• A. $\frac{W_1}{s}$
• B. $\frac{[W_1+\frac{W}{4}]}{s}$
• C. $\frac{[{3W}_1+\frac{W}{4}]}{s}$
• D. $\frac{W_1+W}{4}$

Answer 1

The correct option is B $\frac{[W_1+\frac{W}{4}]}{s}$

stress $=\frac{\text{Tension}}{\text{Area}}$

Tension at the helght $\frac{L}{4}$ from lower end is $=w_1+\frac{3W}{4}$

stress $=\frac{w_1+3w/4}{3}s=$ area of cross-seetion of

Hence (B) option is correct