We are asked to express the dimension of mass in terms of the chosen base quantities: $[V], [T], [F]$ where velocity, time, and force are treated as fundamental quantities.

Write the usual dimensional formulas:

• Velocity: $[V] = [LT^{-1}]$
• Time: $[T] = [T]$
• Force: $[F] = [MLT^{-2}]$

Assume mass can be written as: $[M] = [F]^a [T]^b [V]^c$

Substitute the standard dimensions of each quantity: $[M] = (MLT^{-2})^a (T)^b (LT^{-1})^c$

Expand powers: $[M] = M^a L^{a+c} T^{-2a+b-c}$

Compare exponents with the left-hand side, which is just: $[M^1 L^0 T^0]$

So we get the equations:

• For $M$: $a = 1$
• For $L$: $a + c = 0$
• For $T$: $-2a + b - c = 0$

Solve these equations:

• From $a=1$
• Then $1 + c = 0 \Rightarrow c = -1$
• Now: $-2(1) + b - (-1) = 0$ $-2 + b + 1 = 0$ $b = 1$

Therefore, $[M] = [F]^1 [T]^1 [V]^{-1}$ $[M] = [FTV^{-1}]$

Match with the options:

• A: $[FT^{-1}V^{-1}]$
• B: $[FTV^{-1}]$
• C: $[FT^2V]$
• D: $[FVT^{-1}]$

Hence the correct option is: $\boxed{B}$