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2.1

Given that the speed of light, v, in a fluid depends on an elastic modulus, T. with

dimensions ML-'T-2 and the fluid density, p, in the form v = (T)°(p). If this is to be a

dimensionally homogeneous equation, determine the values of a and b and write the

simplest form of an equation for the speed of light, W.

(4)

Respuesta :

Answer:

Explanation:

[tex]v = T^a\times \rho^b[/tex]

Using dimensional formula on both sides ,

LT⁻¹ = [tex](ML^{-1}T^{-2})^a(ML^{-3})^b[/tex]

= [tex]M^{a+b}L^{-a-3b}T^{-2a}[/tex]

equating the power of equal terms

- 2 a = -1

a = 0.5

-0.5 -3b = 1

3b = -1.5

b = -0.5

a + b = 0

Hence

a = 0.5

b = -0.5

[tex]v=\sqrt{\frac{T}{\rho} }[/tex]

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