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A uniform wire of length L and total weight W is fixed rigidly at one end to the ceiling. A load of weight W₁ hangs from the free lower end. If S is the cross-sectional area of the wire, what is the tensile stress at a point that is (3L/4) above the lower end?

1. W₁/S
2. [W₁ + (W/4)] / S
3. [W₁ + (3W/4)] / S
4. (W₁ + W) / S

Correct answer: [W₁ + (3W/4)] / S

Solution

At a cross-section located 3L/4 above the lower end, the portion of wire below it has length 3L/4 and weight (3L/4)/L * W = 3W/4. The section must support this wire segment plus the hanging weight W₁. Total tension at that section = W₁ + 3W/4. Stress = Tension/S = [W₁ + (3W/4)] / S.

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