Question

One end of a uniform rope of length L and of weight w is attached rigidIy to a point in the roof and a weight w${}_1$ is suspended from its lower. If s is the area of cross-section of the wire, the stress in the wire at a height $\frac{3L}{4}$ from its lower end is:

• A. $\frac{w}{s}$
• B. $\frac{w_1+\frac{w}{4}}{s}$
• C. $\frac{w_1+\frac{2w}{4}}{s}$
• D. $\frac{w_1+w}{s}$

Answer 1

Answer: (B)

$\frac{w_1+\frac{w}{4}}{s}$

Weight of the rope = $w$

Weight at the point A $=\frac{w}{4}$

Area of cross section = $s$

Downward force of A $=\frac{w}{4}+w_1$

Stress in the wire at A $=\frac{\text{force}}{\text{area of cross section}}=\frac{\frac{w}{4}+w_1}{s}$