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.
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Normal stress: It is the restoring force per unit area perpendicular to the surface of the body.
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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)
\(⇒ S_Q=\frac{Force}{\pi r^2_{Q}}\) ------ (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)