Question

how to find dimensions of linear momentum and surface tension in terms of velocity density and frequency

Answer 1

It can be solved with help of using dimension concepts .
Dimension of linear momentum, P = [ MLT⁻¹]
Dimension of velocity, v = [LT⁻¹]
Dimension of density, d = [ML⁻³]
Dimension of frequency , f = [T⁻¹]

Let relation between linear momentum , velocity , density and frequency is
P = $\bold{v^ad^bf^c}$
$\bold{[MLT^{-1}]=[LT^{-1}]^a[ML^{-3}]^b[T^{-1}]^c}$
$\bold{[MLT^{-1}]=[M^b][L^{a-3b}][T^{-a-c}]}$
Compare both sides,
b = 1 ,
a - 3b = 1 ⇒a - 3×1 = 1 ⇒a = 4
- a - c = -1 ⇒-4 - c = -1 ⇒c = -3

Hence , relation is linear momentum, P = $\bold{\frac{velocity^4.density}{frequency^3}}$

Similarly you can got the relation between , surface tension , velocity , density and frequency .
Dimension of surface tension = [MT⁻²]
∴[MT⁻²] = [LT⁻¹]ᵃ [ML⁻³]ᵇ [T⁻¹]ˣ
= [Mᵇ ][Lᵃ⁻³ᵇ] [T⁻ᵃ⁻ˣ]
Compare both sides,
b = 1
a - 3b = 0⇒a = 3
-a - x = -2 ⇒x = -1

Hence, relation is surface tension = $\bold{\frac{velocity^3.density}{frequency}}$

Answer 2

Answer:

Explanation:

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