Question

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

• A. $\left[V^{-2}{A}^2{F}^2\right]$
• B. $\left[V^{-2}{A}^2{F}^{-2}\right]$
• C. $\left[V^{-4}{A}^{-2}F\right]$
• D. $\left[V^{-4}{A}^{2}F\right]$

Answer 1

Answer: (D)

Let $Y=f\left(V,F,A\right)$
$Y=K{V}^x{F}^y{A}^z,K\to$ Unit less
$\left[Y\right]={\left[V\right]}^x{\left[F\right]}^y{\left[A\right]}^z$
$\left[M{L}^{-1}{T}^{-2}\right]={\left[L{T}^{-1}\right]}^x{\left[ML{T}^{-2}\right]}^y{\left[L{T}^{-2}\right]}^z$
$\left[M\right]\left[L^{-1}\right]\left[T^{-2}\right]={\left[M\right]}^y\left[L^{x+y+z}\right]\left[T^{-x-2y-2z}\right]$
$\Rightarrow y=1,x+y+z=-1;-x-2y-2z=-2$
$x+z=-2x+2y+2z=2$
$z=2,x=-4x+2z=0$
$\left|Y\right|=\left[V^{-4}{A}^{2}F\right]$