Question

If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :

• A. $\left[P{A}^{-1}{T}^{-2}\right]$
• B. $\left[P{A}^{1/2}{T}^{-1}\right]$
• C. $\left[P^{2}A{T}^{-2}\right]$
• D. $\left[P^{1/2}A{T}^{-1}\right]$

Answer 1

Answer: (B)

Let $[E]=[P{]}^x[A{]}^y[T{]}^z$
$M{L}^2{T}^{-2}={\left[ML{T}^{-1}\right]}^x{\left[L^2\right]}^y[T{]}^z$
$M{L}^2{T}^{-2}=M^x{L}^{x+2y}{T}^{-x+2}$
$\to x=1$
$\to x+2y=2$
$1+2y=2$
$y=\frac{1}{2}$
$\to -x+z=-2$
$-1+z=-2$
$z=-1$
$[E]=\left[P{A}^{1/2}{T}^{-1}\right]$