If force [F] acceleration [A] time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

Options

A. `[FAT^2]`
B. `[FAT^(-1)]`
C. `[FA^(-1)T]`
D. `[FAT]`

Answer

A

Explanation

`E=kF^(a) A^(b) T^c`
`[M^1 L^2T^(-2)]=k [M^1 L^1T^(-2)]^a [L^1T^(-2)]^(b)[T]^c`
`[M^1 L^2T^(-2)]=k [M^(a) L^(a+b)T^(-2a -2b+c)]`
By comparison, `a = 1 " "…(i)`
`a + b = 2 " "…(ii)`
`-2a - 2b + c = -2 " "…(iii)`
From (i), (ii) and (iii)
`a = 1 , b = 1`
`-2 - 2 + c = -2`
`:. c = + 2`
`E = F^(1) A^(1) T^(2)`