First slide

Elastic Modulie

Question

A steel rod has a cross sectional area of $2 c m^{2}$ . If the rod is subjected to a tensile force of $10^{4} N$ and Young's modulus of steel is $2 \times 10^{11} N / m^{2}$ , what is the elastic potential energy stored per unit volume of the rod?

Easy

A

12 $K J / m^{3}$
B

25 $K J / m^{3}$
C

6.25 $K J / m^{3}$
D

3.5 $K J / m^{3}$

Solution

stress $σ = \frac{1 O^{4}}{2 \times 10^{- 4}} N / m^{2} = 5 \times 10^{7} N / m^{2}$
$∴ u = \frac{σ^{2}}{2 Y} = \frac{{(5 \times 10^{7})}^{2}}{2 \times 2 \times 10^{11}} J / m^{3} = 6.25 K J / m^{3}$

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