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Grade 12Engineering Entrance Exams

Poisson’s ratio of a material is 0.5 percentage change in its length is 0.04% what is change in percentage of diameter ?

Profile image of Rahul Kumar
12 Years agoGrade 12
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1 Answer

Profile image of Saurabh Koranglekar
6 Years ago

We are given:

Poisson’s ratio (ν) = 0.5
Percentage change in length (longitudinal strain) = 0.04%
Step 1: Recall the relationship between Poisson's ratio and lateral strain
Poisson’s ratio (ν) is defined as:

ν = - (lateral strain) / (longitudinal strain)

Where:

Lateral strain = change in diameter / original diameter
Longitudinal strain = change in length / original length
Step 2: Substitute known values
Given ν = 0.5 and longitudinal strain = 0.04%, we can rearrange the formula:

Lateral strain = -ν × Longitudinal strain
Lateral strain = - 0.5 × 0.04%
Lateral strain = - 0.02%

Step 3: Interpretation
The negative sign indicates the diameter decreases when the material is stretched. Thus, the percentage decrease in diameter is 0.02%.

Final Answer: The percentage decrease in diameter is 0.02%.


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