Question

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and $W_1$ weight is suspended from looser end. If A is area of cross-section of the wire, the stress in the wire at a height $\frac{L}{4}$ from the upper end is:

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

Answer 1

The correct option is D $\frac{4W_1+3W}{a}$

$\begin{array}{c}\text{Weight of wire}=w\\ \text{Weight of load}=w_1\\ \text{Area of oross section}=A\\ \text{At a distance of}\frac{L}{4}\text{from the upper end}\\ \text{the}F\text{acting is}\\ F=\left(\frac{w}{L}\right)\left(\frac{3L}{4}\right)+w_1\\ \text{weight of lower}\\ \text{part of string}\\ \therefore \text{Stress at}\frac{L}{4}\text{distance from wpper end}\\ =\frac{4w_1+3w}{A}\end{array}$