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

If frequency (F), velocity (v) and density (D) are considered as funda

1.	If frequency (F), velocity (v) and density (D) are considered as fundamental units the dimensional formula for momentum will be.....
Answer» `D^(2)v^(2)F^(2)` `D^(1)v^(4)F^(-3)` `D^(-1)v^(-4)F^(-3)` `D^(1)v^(1)F^(-2)` Solution :`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)`