# Homework Help: Dimension of length using h,G,c

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1. Dec 26, 2017

### Pushoam

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Dimension of length using h,G,c

[h] = [F r]

$[G] =[ \frac { Fr^2}{m^2} ] \\ [\frac { hG}c] = [L]$

So, the answer is option (b).

Is this correct?

2. Dec 26, 2017

### Pushoam

Mistake: [h ] $\neq$ [Fr]

[h] = [mv r]

[L] = [ $\sqrt{ \frac { hG}{c^3}}]$

Is this correct?

3. Dec 26, 2017

### rude man

Keep guessing & if we say 'yes' or 'no' you'll eventually hit it, won't you?
So rather than answer 'yes' or 'no' we prefer that you show how you arrived at your answer.
BTW why do you distinguish "r" from "L"? They're the same. For example, [G] =M-1L3T-2 etc. , don't need the "r". In SI (mks) there are only 4 dimensions, to wit, M,L,T and Q. (In cgs there are only the first three).

4. Dec 26, 2017

### haruspex

Yes, but as rude man says your working would be clearer if you were to first reduce all the parameters to the standard set M, L, T... and introduce unknowns for the exponents of tne parameters.

5. Dec 27, 2017

### Pushoam

I felt that I could solve the question without converting the dimensions into M,L,T. So, I went that way. I had the impression that that approach is faster. It may be that this impression is wrong.
I think you are suggesting me to do the following way:
I should write dimensions of G, h, c in M,L, T respectively.
And then I should solve the following dimensional equation.
[L] = $[G]^p[h]^q [c]^r$
I will get one equation for each dimension. This will give me the values of p,q,r. Thus I will reach the answer.