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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.Pushoam said:Is this correct?
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.rude man said: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).
The dimension of length using h, G, and c is known as the Planck length, which is equal to approximately 1.62 x 10^-35 meters.
h, G, and c are fundamental constants in physics that are used to calculate the Planck length. h is the Planck constant, G is the gravitational constant, and c is the speed of light in a vacuum.
These constants are important because they provide a universal standard for measuring length in the subatomic realm. They are used in theories such as quantum mechanics and general relativity to describe the fundamental properties of the universe.
Yes, the Planck length is believed to be the smallest possible unit of length and is thought to be the scale at which quantum effects become significant.
The Planck length is so small that it has no practical applications in everyday life. However, understanding this dimension can help us better understand the fundamental structure of the universe and how it operates on a subatomic level.