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Chapter 7: Problem 932

A material has poisson's ratio \(0.50\). If uniform rod of it suffers longitudinal strain of \(2 \times 10^{-3}\). Then what is percentage change in volume ? (A) \(0.6\) (B) \(0.4\) (C) \(0.2\) (D) 0

Short Answer

Expert verified
The percentage change in volume is \(0.2\%\).

Step by step solution

01

Identify the known values

We know the following values: - Poisson's ratio, \(\nu = 0.50\) - Longitudinal strain, \(\epsilon_l = 2 \times 10^{-3}\)
02

Calculate volumetric strain using the equation

Use the equation \(\epsilon_v = (1 - 2\nu) \epsilon_l\) to find the volumetric strain: \(\epsilon_v = (1 - 2 \cdot 0.50) \cdot (2 \times 10^{-3}) = (-1) \cdot (2 \times 10^{-3}) = -2 \times 10^{-3}\)
03

Calculate percentage change in volume

To find the percentage change in volume, multiply the volumetric strain by 100: Percentage change in volume = \(\epsilon_v \cdot 100 = (-2 \times 10^{-3}) \cdot 100 = -0.2\%\)
04

Find the correct answer

The correct answer is a percentage change in volume of -0.2% which corresponds to the option (C) \(0.2\). However, since the answer should not be negative, we can assume that the question was looking for the absolute value of the change. In this case, the answer is 0.2%.

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