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Strength of Materials

Elastic Constants

A metallic ro...

Question

A metallic rod of 500 mm length and 50 mm diameter when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5 mm and a reduction in its diameter by 0.015 mm. The Poisson's ratio of the rod material is
0.3

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Solution

The correct option is A 0.3
$ν = - \frac{L a t e r a l s t r a i n}{L o n g i t u d i n a l s t r a i n} = - \frac{(\frac{Δ D}{D})}{(\frac{Δ L}{L})}$
$ν = (\frac{L}{D}) (- \frac{Δ D}{Δ L})$

Given, L=500 mm, D=50 mm,

$Δ D = - 0.015, Δ L = 0.5 m m$

$∴ ν = \frac{500}{50} \times \frac{0.015}{0.500} = 0.3$

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