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 W₁ 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. $\frac{W_{1}}{S}$
• B. $\frac{W_{1} + (W/4)}{S}$
• C. $\frac{W_{1} + (3W/4)}{S}$
• D. $\frac{W_{1} + W}{S}$

Answer 1

Answer: (C)

$\frac{W_{1} + (3W/4)}{S}$

Answer 2

As the wire is uniform so the weight of wire below point P is $\frac{3W}{4}$

∴ Total force at point $P = W_{1} + \frac{3W}{4}$ and area of cross-section = S

$\therefore$ Stress at point P $= \frac{\text{Force}}{\text{Area}} = \frac{W_{1} + \frac{3W}{4}}{S}$