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  4. A metal rod of Young's modulus 2 × 1010 Nm -2 undergoes an elastic strain of 0.06 % . The energy per unit volume stored in Jm -3 is

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Q. A metal rod of Young's modulus $2 \times 10^{10} Nm ^{-2}$ undergoes an elastic strain of $0.06 \% .$ The energy per unit volume stored in $Jm ^{-3}$ is

Mechanical Properties of Solids

Solution:

Energy density $=\frac{1}{2} \times$ stress $\times$ strain
$=\frac{1}{2}(Y \times$ strain $) \times$ strain
$=\frac{1}{2}\left(2 \times 10^{10} Nm ^{-2}\right)\left(\frac{0.06}{100}\right)^{2}$
$=3600 \,Jm ^{-3}$