Physics - Unit & Dimension Question with Solution | TestHub

Let energy $E=F^x{A}^y{T}^3$ Writing the dimensions on both sides $\begin{array}{rl}& \left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]={\left[{\mathrm{MLT}}^{-2}\right]}^x{\left[{\mathrm{LT}}^{-2}\right]}^y[\mathrm{T}{]}^2\\ & \left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]=\left[{\mathrm{M}}^x{\mathrm{L}}^{x+y}{\mathrm{T}}^{-2x-2y+z}\right]\end{array}$ On comparing both sides $\begin{array}{rl}& x=1\\ & x+y=2\\ & \Rightarrow y=2-x=2-1=1\\ & \text{ and }-2x-2y+z=-2\\ & \Rightarrow -2\times 1-2\times 1+z=-2\\ & \Rightarrow z=-2+2+2\\ & =2\\ & \end{array}$ $\therefore$ Dimensional formula of energy $=FA{T}^2$