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

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$\frac{W_{1} + (W / 4)}{S}$

$\frac{W_{1} + (3 W / 4)}{S}$

$\frac{W_{1} + W}{S}$

$\frac{W_{1}}{S}$

answer is C.

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Detailed Solution

As the wire is uniform so the weight of wire below point P is $\frac{3 W}{4}$ .

$∴$ Total force at point $P = W_{1} + \frac{3 W}{4}$

and area of cross-section $= S$

$∴$ Stress at point $P = \frac{F o r c e}{A r e a} = \frac{W_{1} + \frac{3 W}{4}}{S}$

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