If speed \(V,\) area \(A\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be :

\(M ^{1} L ^{-1} T ^{-2}=\left[ MLT ^{-2}\right] x \left[ L ^{2}\right] y \left[ L T ^{-1}\right]^{z}\)

\(M ^{1} L ^{1} T ^{-2}=[ M ]^{ x }[ L ]^{ x +2 y +z}[ T ]^{-2 x - z }\)

comparing power of \(ML\) and \(T\)

\(x=1 \ldots(1)\)

\(x+2 y+z=-1\)\(...(2)\)

\(-2 x-z=-2\)\(...(3)\)

after solving

\(x=1\)

\(y=-1\)

\(z=0\)

\(Y=F A^{-1} V^{0}\)