Still learning dimensional analysis

[help1please]

Homework Statement

angular frequency omega, speed of light and gravitational constant

Homework Equations

Just the expression,

$$\frac{2 \omega c}{\sqrt{G}}$$

The Attempt at a Solution

Still learning dimensional analysis. So I am simply wanting to know if I have done this right. If I have, I get

$$\frac{2 \omega c}{\sqrt{G}}$$

this with dimensions of force, right?

Thanks in advance.

 

[cepheid]

Homework Statement

angular frequency omega, speed of light and gravitational constant

Homework Equations

Just the expression,

$$\frac{2 \omega c}{\sqrt{G}}$$

The Attempt at a Solution

Still learning dimensional analysis. So I am simply wanting to know if I have done this right. If I have, I get

$$\frac{2 \omega c}{\sqrt{G}}$$

this with dimensions of force, right?

Thanks in advance.

I'll use square brackets around a quantity to mean, "dimensions of" that quantity (which is a fairly common notation, I think). Then:

[ω] = time^-1

[c] = length * time^-1

[√G] = [G]^1/2 = (force * length² * mass^-2)^1/2

Therefore [ωcG^-1/2] = length * time^-2 * force^-1/2 * length^-1 * mass

= force^-1/2 * mass * time^-2

= (mass * length * time^-2)^-1/2 * mass * time^-2

= mass^1/2 * length^-1/2 * time^-1

So, no, it doesn't have dimensions of force.

 

[help1please]

What does it have dimensions of then? I mean, other than what you have said, is there a commonly known dimension it exhibits? like energy for instance?

 

[cepheid]

It doesn't correspond to any common physical quantity, and there is no reason that it has to (you've simply come across a new type of quantity),

However, the *square* of the quantity is a common type of quantity. Hint: square everything in blue, and rearrange things to produce "force" plus some leftover stuff. What is the dimension of the quantity you've come up with?