Question

One end of a 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 $3L/4$ from its lower end is

• A. $W_1/S$
• B. $(W_1+\frac{W}{4})S$
• C. $\frac{(W_1+\frac{3W}{4})}{S}$
• D. $(W_1+W)S$

Answer 1

The correct option is C $\frac{(W_1+\frac{3W}{4})}{S}$

Force at a height $\left(3L/4\right)$ from its lower end,
$F=$ Weight suspended + Weight of $\frac{3}{4}$ of the chain
Since the wire is uniform, therefore weight of the lower portion, $W_L=\frac{3L}{4}\times \frac{W}{L}=\frac{3W}{4}$
Force, $F=W_1+\frac{3W}{4}$
Stress, $\sigma =\frac{F}{S}=\frac{W_1+\frac{3W}{4}}{S}$

Hence, the correct answer is option (c)