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(D) Young's modulus $(Y)$ is defined as the ratio of stress to strain. Since strain is dimensionless,the dimension of $Y$ is the same as that of stres

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$V^{-4} A^2 F$

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(D) Young's modulus $(Y)$ is defined as the ratio of stress to strain. Since strain is dimensionless,the dimension of $Y$ is the same as that of stress (Force/Area).$[Y] = [F] / [L^2]$.We are given fundamental units $V, A, F$.We know $F = M \cdot A$,so $M = F \cdot A^{-1}$.Also,$V = L \cdot T^{-1}$ and $A = L \cdot T^{-2}$.Dividing $A$ by $V$: $A/V = (L \cdot T^{-2}) / (L \cdot T^{-1}) = T^{-1}$,so $T = V \cdot A^{-1}$.Now,$L = V \cdot T = V \cdot (V \cdot A^{-1}) = V^2 \cdot A^{-1}$.Therefore,$L^2 = (V^2 \cdot A^{-1})^2 = V^4 \cdot A^{-2}$.Substituting these into the expression for $Y$:$[Y] = [F] / [L^2] = F / (V^4 \cdot A^{-2}) = F \cdot V^{-4} \cdot A^2$.

If speed $(V)$,acceleration $(A)$,and force $(F)$ are considered as fundamental units,the dimension of Young's modulus will be

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