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# Need explanation for: One end of a uniform wire of length L and of weight W is attached rigidly to a point on the roof and a weight W1 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

One end of a uniform wire of length L and of weight W is attached rigidly to a point on the roof and a weight W1 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,

• Option 1)

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

• Option 2)

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

• Option 3)

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

• Option 4)

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

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As discussed in

Stress -

The internal restoring force per unit area of deformed body.

- wherein

Due to the forces, the body gets deformed and internal forces appear.

As discussed in @14070

Total force and height 3L/4 from its lower end = weight suspended + weight of 3/4 of the chain

$= W_{1}+\left ( \frac{3W}{4} \right )$

Option 1)

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

This solution is incorrect.

Option 2)

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

This solution is incorrect.

Option 3)

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

This solution is correct.

Option 4)

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

This solution is incorrect.

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