1.

Calculate the dimensions of impulse in terms of velocity `(upsilon)` denity `(rho)` and frequeny (v) as fundamental units.

Answer» Let impulse, `I = k upsilon^a rho^b v^c …..(i)`
where a, b,c are the dimensions and k is dimen- sionless constant. Writing the dimensions,
`[MLT^(-1)] = (LT^(-1))^a (ML^(-3))^b (T^(-1))^c`
`= M^b L^(a-3b) T^(-a-c)`
Applying the principle of homogeneity of dimensios, we get
b=1,
`a- 3b =1, a = +3b+ 1 =+3 +1 = +4`
`-a - c =-1, c= -a +1 = -4+1 = -3`
Putting these values in (i) we get
`I = k upsilon^4 rho^1 v^(-3) = k(rho upsilon^4)/(v^3)`


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