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 are of cross-section of the wire, the stress in
the wire at a height (3 L /4) from its lower end is :

• A. $W_1/S$
• B. $[W_1+(W/4\left)\right]/S$
• C. $[W_1+(3W/4\left)\right]/S$
• D. $W_1+\left(W\right)/S$

Answer 1

Answer: (C)

$[W_1+(3W/4\left)\right]/S$

$\begin{array}{c}L=\text{length of the wire}\\ W=\text{weight of the wire}\\ S=\text{Area of cross-section}\\ W_1=\text{Weigut suspended}\end{array}$

$\begin{array}{cc}\text{Stress}=\frac{\text{force}}{\text{Area}}& =\frac{\text{Tension}}{\text{Area}}\\ \text{Force at point}& A=W_1+\text{weight of wire}AB\\ f_A& =W_1+\frac{3W}{4}\\ & \therefore \text{Stress}=\frac{(W_1+\frac{3W}{4})}{S}\end{array}$

Hence option C is correct