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

Options

A. `FA^(2)T`
B. `FAT^(2)`
C. `F^(2)AT`
D. `FAT`

Answer

B

Explanation

`E = KF^(a) A^(b) T^(c )`
`[ML^(2)T^(-2)] = [MLT^(-2)]^(a)[LT^(-2)]^(b) [T]^(c)`
`[ML^(2)T^(-2)] =[M^(a) L^(a+b)T^(-2a -2b+c)]`
`:. a = 1, a+ b= 2 rArr b = 1`
and `-2a -2b +c = -2 rArr c = 2`
`:. E = KFAT^(2)`