Question

if density, g and frequency are basic quantities than find dimension of force

Answer 1

The dimension of force is [MLT^-2] & dimension of density is [ML^-3] & for g its [LT^-2] & for frequency its [T^-1].

So First we equate force with respect to all these quantities.

F=[Density]^a [g]^b [Frequency]^c.  (a,b,c are arbitrary)

So

[MLT^-2] = [ML^-3]^(a) *[LT^-2]^(b) *[T^-1]^(c)

[MLT^-2] = M^(a) *L^(-3a+b) *T^(-2b+c)

So by comparison

a=1

-3a+b=1, So b=4

-2b+c=-2 So c=-6

So the final formula is F=[Density]^1*[g]^4*[Frequency]^-6

Hope it helps!!!!