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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
4. Quadrupled 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)

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