Question

P=(pgh)^1/2
here P=pressure
small p(p)=resistivity
h=height

check the equation is dimensionally correct or not??
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Answer 1

Answer:

no

Explanation:

since p has dimension kg/m^3

h has dimension of m for depth and altitude with km.

g has dimension of m/s^2.

By substituting these values it won't satisfy.

Answer 2

Answer:

The given equation is dimensionally incorrect.

Explanation:

Given,

$P = \sqrt{pgh}$  (where P = pressure, p = resistivity, h = height)

Taking L.H.S of the equation:

$Dim(P) = ML^{-1}T^{-2}$.....(1)

Taking R.H.S of the equation:

$Dim(\sqrt{pgh} ) = \sqrt{[ML^3T^{-3}A^{-2}][LT^{-2}][L]}\\\implies Dim(\sqrt{pgh} ) = \sqrt{ML^5T^{-5}A^{-2}} \\\implies Dim(\sqrt{pgh} ) = M^\frac{1}{2} L^\frac{5}{2}T^{-\frac{5}{2} } A^{-1}$......(2)

As we can see clearly from equations (1) and (2), they are not equal.

Hence, the given equation is dimensionally incorrect.