Question

In a system of units if force $(F)$, acceleration $(A)$, and time $(T)$ are taken as fundamental units, then the dimensional formula of energy is:

• A. $F{A}^{2}T$
• B. $FA{T}^2$
• C. $F^{2}AT$
• D. $FAT$

Answer 1

Answer: (B)

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