One end of 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 cross-section of the wire, the st

Question

One end of 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 cross-section of the wire, the stress in the wire at a height ( 3 L /4 ) from its lower end is

TestHub · Accepted Answer

Consider the part of the wire below the point at height $\frac{3 L}{4}$ from the lower end.

Its length is $\frac{3 L}{4}$ , so its weight is $\frac{3 W}{4}$ .

Tension there $= W_{1} + \frac{3 W}{4}$

Stress $= \frac{W _{1} + 3 W /4}{S}$

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