Question

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the ceiling 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. $(W_1+\frac{3W}{4})/S$
• D. $(W_1+W)/S$

Answer 1

The correct option is C

$(W_1+\frac{3W}{4})/S$

Since the wire is uniform, i.e. its mass per unit length is constant over its entire length L, the total downward weight = the weight of the suspended mass + weight of length $\frac{3L}{4}$ of the wire or $F=W_1+\frac{3W}{4}.$

$\therefore Stress=\frac{force}{area}=\frac{F}{S}=\frac{W_1+\frac{3}{4}W}{S}$