Question

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

• A. $F{A}^{2}T$
• B. $FA{T}^2$
• C. $F{A}^2{T}^3$
• D. $FAT$

Answer 1

The correct option is B $FA{T}^2$

Let $E\propto F^x{A}^y{T}^z$

$\Rightarrow \left[E\right]=\left[F{]}^x\right[A{]}^y[T{]}^z$
$\Rightarrow E=\left[ML{T}^2{]}^x\right[L{T}^{-2}{]}^y[T{]}^z$
$\Rightarrow \left[M{L}^2{T}^{-2}\right]=\left[M^x{L}^{x+y}{T}^{-2x-2y+z}\right]$
Equating powers on both sides,
$x=1$
$x+y=2\Rightarrow y=2-1=1$
$-2x-2y+z=-2\Rightarrow -2-2+z=-2\Rightarrow z=2$

$\therefore E\propto FA{T}^2$