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 prop F^(a) A^(b) T^(c)`
`[ML^2 T^(-2) ] =[MLT^(-2)]^(a) [LT^(-2)]^(b) [T]^c`
`=[M^(a) L^(a+b)T^(-2a-2b+c)]`
`a = 1 , a + b = 2 implies b = 1`
`-2 =-2a -2b +c`
`implies -2 =-2 -2 +c implies c = 2`
`E prop FAT^2`