Calculate the dimensions of Force & Impulse in terms of velocity, density & frequency as fundamental units.

Dear student,
Dimension of the force :
$F = \left[M^1{L^1}^{}{T}^{-2}\right]$

Dimension of force in terms of velocity(v) , density(d) and frequency(f) :

$$\begin{gathered} F = \left[v^a{d}^b{f}^c\right] \\ Dimension of velocity : \left[M^0{L}^1{T}^{-1}\right] \\ density: \left[M^1{L}^{-3}{T}^0\right] \\ frequency : \left[M^0{L}^0{T}^{-1}\right] \\ therefore \\ \left[M^1{L}^1{T}^{-2}\right] = \left[M^0{L}^1{T}^{-1}{]}^a\right[M^1{L}^{-3}{T}^0{]}^b\left[M^0{L}^0{T}^{-1}\right] \\ On solving , we get \\ a=4 , b=1, c=-2 \\ therefore \\ F = \left[v^4{d}^1{f}^{-2}\right] \end{gathered}$$

Impulse is defined as the change in momentum , dimension is :

$$\begin{gathered} I = \left[M^1{L}^1{T}^{-1}\right] \\ I = \left[v^a{d}^b{f}^c\right] \end{gathered}$$

similarly we can solve for a,b,c and we get
a=4,  b= 1,  c=-3
$I = [v^4{d}^{1^{}}{f}^{-3}]<br>\; Regards$