One end of a uniform wire of length L and of weight W is...

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 area of crosssection of the wire, the stress in the wire at a height $3 L / 4$ from its lower end is (a) $W_{1} / S$ (b) $\left(W_{1}+\frac{W}{4}\right) S$ (c) $\frac{\left(W_{1}+\frac{3 W}{4}\right)}{S}$ (d) $\left(W_{1}+W\right) S$

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 area of crosssection of the wire, the stress in the wire at a height $3 L / 4$ from its lower end is
(a) $W_{1} / S$
(b) $\left(W_{1}+\frac{W}{4}\right) S$
(c) $\frac{\left(W_{1}+\frac{3 W}{4}\right)}{S}$
(d) $\left(W_{1}+W\right) S$

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Key Concepts

Stress

Stress is defined as the force exerted per unit cross?sectional area. It gives a measure of the internal forces in a material when an external force is applied, and in this context, it is calculated by dividing the tension (force) by the cross?sectional area of the wire.

Tension in Vertical Cables

In a vertical cable or wire under gravity, the tension at any point is equal to the total weight of all the loads and the portion of the cable below that point. This concept is crucial for understanding how forces vary along the length of a hanging wire, as each point must support the cumulative weight beneath it.

Weight Distribution in a Uniform Wire

A uniform wire has weight that is evenly distributed along its length. This means that the weight of any segment of the wire is proportional to its length. When analyzing forces at a given point along the wire, one must account for the fraction of the total weight corresponding to the length of the wire that is hanging below that point.

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