An aluminium rod with Young's modulus undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is [2023]

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Solution

Q.
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 [2023]

1 11200

2 2800

3 5600

4 8400

Ans.
(3)

$Y = 7 \times 10^{10} {N/m}^{2}$

$Strain = \frac{0.04}{100}$

$Energy = \frac{1}{2} (\frac{Y A}{ℓ}) {(Δ x)}^{2}$

$Energy = \frac{1}{2} Y A {(\frac{Δ x}{ℓ})}^{2} \times ℓ$

$\frac{E}{V} = \frac{1}{2} \times Y \times {strain}^{2} = \frac{1}{2} \times 7 \times 10^{10} \times \frac{0.04 \times 0.04}{10^{4}} = 56 \times 10^{2}$

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