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

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Elasticity & SHM

An aluminium rod with Young's modulus

Y = 7.0 \times 1 0^{10} N / m^{2}

undergoes elastic strain of

0.04%

. The energy per unit volume stored in the rod in SI unit is:

Answer: (A)

The elastic energy per unit volume (energy density) stored in a material is:

u = \frac{1}{2} Y (strain)^{2}

Given:

Y = 7.0 \times 1 0^{10}

N/m², strain

= \frac{0.04}{100} = 4 \times 1 0^{- 4}

u = \frac{1}{2} \times 7.0 \times 1 0^{10} \times (4 \times 1 0^{- 4})^{2}

u = \frac{1}{2} \times 7.0 \times 1 0^{10} \times 16 \times 1 0^{- 8}

u = 3.5 \times 16 \times 1 0^{2} = 56 \times 1 0^{2} = 5600

J/m³

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Single correct option