Question

Ratio of radius of two wires in 2:1apply same force what in ratio of their stress

Answer 1

Explanation:

Given Ratio of radius of two wires is 2:1 if same force is applied what is the ratio of their stress

• We know that
• Stress = Force / Area of cross section
• Area of cross section depends on square of radius, so the ratio of areas is 4:1. Therefore Stress is inversely proportional to area
• So the ratio of stresses will be 1:4  
• There are two wires and are stretched in equal forces. So there will be a stress or an extension.
• So stress σ = P / A (force / unit area)
• So σ is proportional to 1/A  
• Or σ is proportional to 1/R^2
• So now stress of both wires will be σ1 / σ2 = R2^2 / R1^2
•                                                                     = R1^2 / (2 R2)^2 (since R1/R2 = 2/1)
•                                                                     = R2^2 / 4 R2^2

                    Therefore σ 1 / σ 2 = 1/4 or 1:4

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