If frequency (F), velocity (v) and density (D) are considered as fundamental units the dimensional formula for momentum will be.....

Options

A. `D^(2)v^(2)F^(2)`
B. `D^(1)v^(4)F^(-3)`
C. `D^(-1)v^(-4)F^(-3)`
D. `D^(1)v^(1)F^(-2)`

Explanation

`P prop F^(a)v^(b)D^(c)`
`:.P=KF^(a)v^(b)D^(c)` where `K ne 0` dimensionless onstant.
`:. A,b ne0 and a,b,c, in R`
Comparing both the sides
`:. M^(1)L^(1)T^(1)=(T^(-1))^(a)(L^(1)T^(-1))^(b)(M^(1)L^(-3))^(c)`
`=T^(-a)xxL^(b)xxM^(c)L^(-3c)`
`=M^(-c)xxL^(b-3c)T^(-a-b)`
`:.` Comparing power of M,L,T
`:. 1=c " " :. c=I`
`:. 1=b-3c=b-3 " " :.b=4`
`:. a=1-b=1-4=-3 " " :.a=-3`
`:.` Dimensional formula of momentum in new system is
`P=K F^(a)v^(b)D^(c)`
`K=1, a=-3,b=4,c=1`
`:.[P]=F^(-3)v^(4)D^(1)`
`:.[P]=D^(1)v^(4)F^(-3)`