A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of 2 × 10^–3, then the percentage increase in its volume is

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10%

20%

answer is A.

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Detailed Solution

To find the percentage increase in the volume of a rod when it experiences a longitudinal strain, we can use the relationship between longitudinal strain, Poisson's ratio, and the volumetric strain.

σ = 0.5

$\frac{∆ l}{l} = 2 x 10^{- 3}$

$\frac{∆ V}{V} x 100 = [(1 - 2 σ) \frac{∆ l}{l}] x 100 = 0 %$

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