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An aluminium rod with Young's modulus $Y = 7.0 \times 10 ^{10} N/m^{2}$ undergoes elastic strain of $0.04%$ . The energy per unit volume stored in the rod in $SI$ unit is:
Option: 1
$5600$

Option: 2
$2800$

Option: 3
$11200$

Option: 4
$8400$

Answers (1)

best_answer

Aluminium rod Young’s modulus
$\mathrm{y}=7.0 \times 10^{10} \frac{\mathrm{N}}{\mathrm{m}^2}$
strain $0.04%$
strain $= \frac{0.04}{100}$
Energy per unit volume $= \frac{1}{2}$ stress $\times$ strain
$= \frac{1}{2} y$ strain $\times$ strain
$= \frac{1}{2}y\left ( strain \right )^{2}$
$=\frac{1}{2} \times 7 \times 10^{10} \times\left(\frac{0.04}{100}\right)^2$
Energy per unit volume $= 5600 \frac{J}{ m^{3}}$

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