Question

Check the correctness of the relation

h = r p g / 2 s cos(theta) , where h = height, r = radius, p = density, s = surface tension, and g = acceleration due to gravity.

Answer 1

Answer:

Given relation is incorrect.

Explanation:

Given that,

$h= \dfrac{r\rho g}{2s cos\theta}$

The units of s,r,g and density

Surface tension $S=[M][T]^{-2}$

Radius $R= [L]$

Density $\rho=[M][L]^{-3}$

Gravity due to acceleration $g=[L][T]^{-2}$

$h= \dfrac{r\rho g}{S}$

$h= \dfrac{ [L]\times [M][L]^{-3}\times[L][T]^{-2}}{[M][T]^{-2}}$

$h=[L^{-1}]$

This relation is incorrect.

The correct relation is define as:

$h= \dfrac{2scos\theta}{r\rho g}$.....(I)

Now put the all value in equation (I)

$h= \dfrac{S}{r\rho g}$

$h= \dfrac{[M][T]^{-2}}{ [L]\times [M][L]^{-3}\times[L][T]^{-2}}$

$h=[L]$

This relation is correct.

Hence, Given relation is incorrect.

Answer 2

Answer:

The given relation is incorrect.

Explanation:

It is given that,

$h=\frac{rpg}{2cos(theta)}$

h=height, r=radius, p=density, s=surface tension, and g=acceleration due to gravity.

The dimensions of the above given quantities are as follows:
Surface tension=[M][L]⁻²

Radius=[L]

Density=[M][L]⁻³

g=[L][T]⁻²

Cosθ has no dimensions.

On substituting the dimensions in the given equation, we get

$h=\frac{[L]*[M][L]^{-3}*[L][T]^{-2} }{[M][T]^{-2} }$

∴h=[L]⁻¹

This relation is incorrect.

For the relation to be correct,

$h=\frac{2cos(theta)}{rpg}$