First slide

Elastic Modulie

Question

The youngs modulus of the material of a rod is 20 ×10¹⁰ pascal. When the longitudinal strain is 0.04%, The energy stored per unit volume is

Moderate

A

4 × 10^–3 J/m³
B

8 × 10³ J/m³
C

16 × 10^–3 J/m³
D

16 × 10³ J/m³

Solution

$\large y = 20 \times {10^{10}}N/{m^2};\;\frac{{\Delta \ell }}{\ell } = \frac{{0.04}}{{100}} = 4 \times {10^{ - 4}}$
$\large \frac{W}{V} = \frac{1}{2}Y{(strain)^2} = \frac{1}{2} \times 20 \times {10^{10}} \times 16 \times {10^{ - 8}}$
$\large = 16 \times {10^3}J/{m^3}$

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