Is the Young's Modulus Equation Homogeneous?

[Frozenblaze1]

Homework Statement

I'm doing an experiment to determine the young's modulus involving the following equation:

Homework Equations

The Attempt at a Solution

Finding the base units of the young's modulus with the equation resulted in the young's modulus being dimensionless, which of course is not true.

Further attempts to check if the equation is homogeneous resulted in the equation not being homogeneous. Can someone double check whether or not this is the case?

 

[mfb]

The difference between two values with units kg/m is a value with units kg/m.

If it happens to be exactly zero, then some quantity is zero, but that is not part of the dimensional analysis.

 

[Frozenblaze1]

The difference between two values with units kg/m is a value with units kg/m.

If it happens to be exactly zero, then some quantity is zero, but that is not part of the dimensional analysis.

You're right, that's a mistake.

I've worked out the base units again and this is what i got.

$$\frac{m}{y} = \frac{8.π.r^2.ϒ.y^2}{g.L^3} + \frac{4.T}{L.g}$$

$$\frac{kg}{m} = \frac{kg.m^5.s^-2}{m^4.s^-2} + \frac{kg}{m}$$

$$\frac{kg}{m} = kg.m + \frac{kg}{m}$$
This means the equation is not homogeneous right? Or is there a mistake somewhere?

 

[mfb]

Check the units of Young's modulus.

 

[Chestermiller]

I checked the units in your equation, and they look OK to me.

 

[mfb]

The equation in post 1 ("Relevant equations") has matching units. The calculation in post 3 has a mistake.

 

[Frozenblaze1]

Yeah, I was taking the value of the Young's from google which seems to be incorrect. It should be kg.m^-1.s^-2

 

[mfb]

Strange, https://en.wikipedia.org/wiki/Young's_modulus]the[/PLAIN] actual Wikipedia article has the right units. Some bug at Google's preview.