First slide

Elastic Modulie

Question

A uniform metal rod of 2 mm² cross-section is heated from 0 °C to 20°C. The coefficient of linear expansion of the rod is 12 x 10^-6/ °C. Its Young's modulus of elasticity
is 10¹¹ N /m² . The energy stored per unit volume of the rod is:

Easy

A

$2880 J / m^{3}$
B

$1500 J / m^{3}$
C

$5760 J / m^{3}$
D

$1440 J / m^{3}$

Solution

Energy stored per unit volume
$= \frac{1}{2} \times Y \times {(strain)}^{2} = \frac{1}{2} \times Y \times {(α ∆ θ)}^{2} = \frac{1}{2} \times 10^{11} \times {(12 x 10^{- 6} \times 20)}^{2} = 2880 J / m^{3} .$

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