What is called elastic energy density? Write its formula and dimensional formula.
(N/A) Elastic energy density is defined as the elastic potential energy stored per unit volume of a material when it is deformed.
Formula: $u = \frac{1}{2} \times \text{stress} \times \text{strain} = \frac{1}{2} \times Y \times (\text{strain})^2$,where $Y$ is Young's modulus.
Dimensional formula: Since energy density is $\frac{\text{Energy}}{\text{Volume}}$,its dimensions are $[M L^2 T^{-2}] / [L^3] = [M L^{-1} T^{-2}]$.
Formula: $u = \frac{1}{2} \times \text{stress} \times \text{strain} = \frac{1}{2} \times Y \times (\text{strain})^2$,where $Y$ is Young's modulus.
Dimensional formula: Since energy density is $\frac{\text{Energy}}{\text{Volume}}$,its dimensions are $[M L^2 T^{-2}] / [L^3] = [M L^{-1} T^{-2}]$.
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