If force `(F)` velocity `(V)` and time `(T)` are taken as fundamental units, then the dimensions of mass are

Options

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

Answer

D

Explanation

(4) `m prop F^(a) V^(b) T^(c )`
`prop [MLT^(-2)]^(a) [LT^(-1)]^(b) [T]^(c )`
`M^(1) L^(0) T^(0) prop M^(a) L^(a + b) T^(- 2a - b -c)`
Comparing powers of `M, L` and `T`, we get
`M : a = 1`
`L : a + b = 0 implies b = - 1`
`T : - 2a - b - c = 0`
`-2 + 1 - c = 0 implies c = 1`
`m prop F^(1) V^(-1) T^(-1)`
`m = [FV^(-1) T]`