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

Options

A. `[P^1 A^(-1) T^1]`
B. `[P^2 A^1 T^1]`
C. `[P^1 A^(-1//2) T^1]`
D. `[P^1 A^(1//2) T^(-1)]`

Answer

D

Explanation

Let energy , `E prop P^a A^b T^c`
or `E=kP^a A^b T^c`
or `[ML^2 T^(-2)]=[MLT^(-1)]^a [L^2]^b[T]^c = [M^a L^(a+2b)T^(-a+c)]`
whence , a=1 , b=`1/2` , c=-1
Dimensional formula for E is `[P^1 A^(1//2) T^(-1)]`