Question

In a system of units of 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

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

Energy $=M{L}^2{T}^{-2}=\left[F{]}^a\right[A{]}^b[T{]}^c=[ML{T}^{-2}{]}^a\left[L{T}^{-2}{]}^b\right[T{]}^c$
$M{L}^2{T}^{-2}=M^a{L}^{a+b}{T}^{-2a-2b+c}$
$a=1,a+b=2$
$-2a-2b+c=-2$
$\therefore b=1$ and $c=2$