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

The correct option is A $F{A}^{2}T$

Consider that the energy is expressed as:

$E=K{F}^a{A}^b{T}^c$

Substituting the dimensional formulas:

$\left[M{L}^2{T}^{-2}\right]=\left[ML{T}^{-2}{]}^a\right[L{T}^{-2}{]}^b[T{]}^c$

$\left[M{L}^2{T}^{-2}\right]=\left[M^a{L}^{a+b}{T}^{-2a-2b+c}\right]$

$\Rightarrow a=1,a+b=2\Rightarrow b=1$

and $-2a-2b+c=-2\Rightarrow c=2$

$\therefore E=KFA{T}^2$