Energy density  = $[ {\frac{{workd\,done}}{{volume}}} ] = \frac{{ML{T^{ – 2}} \cdot L}}{{{L^3}}} = [ {M{L^{ – 1}}{T^{ – 2}}}$
 Young's  modulus = $\left[ Y \right] = \left[ {\frac{{Force}}{{Area}}} \right] \times \frac{{\left[ l \right]}}{{\left[ {\Delta l} \right]}}$
$= \frac{{ML{T^{ – 2}}}}{{{L^2}}}\, \cdot \frac{L}{L} = \left[ {M{L^{ – 1}}{T^{ – 2}}} \right]$
The dimensionsof $1$ and $4$ are the same.