# If two wire P and Q are streched by equal load and the radius of P is two times the radius of Q then the stress on P will be:

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If two wire P and Q are streched by equal load and the radius of P is two times the radius of Q then the stress on P will be:
1. Remains same as of Q
2. Halved as of Q
3. One-fourth as of Q

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Correct Answer - Option 3 : One-fourth as of Q

CONCEPT:

Stress (S):

• Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
• The standard unit of stress is N/m.

$⇒ Stress =\frac{Force(F)}{Area (A)}$

• When a rod or wire pulled from both sides then the stress generated is tensile stress.
• Normal stress: It is the restoring force per unit area perpendicular to the surface of the body.
• Tangential stress: When the elastic restoring force or a deforming force acts parallel to the surface area, the stress is called tangential stress.

EXPLAINATION:

Given - Force of wire P = Force on wire Q and Radius of P (rp) = 2rQ

• From the above, it is clear that stress is written as:

$⇒ Stress =\frac{Force(F)}{Area (A)}$

• Since stress is inversely proportional to the area, and the area is proportional to the square of the radius. Therefore, stress is the directly proportional square of the radius.
• Now the ratio of the stress of both wire can be expressed as:
• Stress for wire P is,

$⇒ S_P=\frac{Force}{\pi r^2_{P}} = \frac{Force}{4\pi r^2_{Q}}$    ------ (1)

• Stress for wire Q is,

$⇒ S_Q=\frac{Force}{\pi r^2_{Q}}$    ------ (2)

On diving equation 1 and 2, we get

$⇒ \frac{S_P}{S_Q}=\frac{1}{4}$

$\Rightarrow S_P=\frac{1}{4}\times S_Q$

• Therefore, stress on P is one-fourth the stress on Q. Hence, The correct option is (3)