If frequency `F`, velocity `V` , and density `D` are considered fundamental units , the dimensional formula for momentum will be

Options

A. `DVF^(2)`
B. `DV^(2)F^(-1)`
C. `D^(2)V^(2)F^(2)`
D. `DV^(4)F^(-3)`

Answer

D

Explanation

`P=mv=FvD`
`MLT^(-1)=F^(x)V^(y)D^(z)=[T^(-1)]^(x)[LT^(-1)]^(y)[ML^(-3)]^(z)=[T^(-x)][L^(y)T^(-y)][M^(z)L^(-3z)]`
Equating the powers we get
`z=1,y=4,x=-3`
`:.P=F^(-3)v^(4)D^(1)`