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“What are the limitations of homogenity?”
The question is acutually”What are the limitations of dimensional analysis?”
The dimensional analysis is based on the principle of homogenity of dimensions. The question is already discussed earlier HERE
Nijisha’s Question: There are various forces we see in nature, and among them, gravitational force is the weakest. If we think about it ,the entire earth is pulling on us and yet we can manage to pick thinks up. I’ve heard somewhere that we can explain this weakness of gravitational force with the help of extra dimensions ( Something related to M theory? ). Can you explain this theory ?
It’s a little bit difficult to discuss in detail the M theory in detail as such at School level. However, I’ll try to give a brief idea about it.
M-theory is an extension of string theory in which 11 dimensions are identified. This is a theory currently in development
To quote from Wikipedia:
“In the 1980s, a new mathematical model of theoretical physics called string theory emerged. It showed how all the particles, and all of the forms of energy in the universe, could be constructed by hypothetical one-dimensional “strings,” infinitely small building-blocks that have only the dimension of length, but not height or width. Further, string theory suggested that the universe is made up of multiple dimensions. We are familiar with height, width, and length as three dimensional space, and time gives a total of four observable dimensions. However, string theories initially supported the possibility of ten dimensions—the remaining 6 of which we can’t detect directly. This was later increased to 11 dimensions based on various interpretations of the ten dimensional theory”
In M-theory may stand for membrane. (Some claim M for mother, matrix,mystery etc)
M-Theory brought all of the string theories together. It did this by asserting that strings are really 1-dimensional slices of a 2-dimensional membrane vibrating in 11-dimensional space.
Though M – Theory is developed mathematically, it is not proved physically. Scientists and Mathematicians take M-Theory as the only theory developed so far which can explain all the aspects of Universe (or multiverse) as a whole. But, I am sure, new theories will come and take over as we develop our understanding further.
Stephen Hawking’s New work The Grand Design talks about the Multiverse and the God’s intervention in the creation of Universe (which he says not necessary)
(I fear that I’ve brought more unknowns in explaining the one unknown. However, it will be good if the discussion goes on.)
What is the difference between capital ‘G’ and small ‘g’ in the chapter gravitation?
|Acceleration due to gravity||Universal constant of gravitation|
|varies from place to place||A constant everywhere on earth|
|vector quantity||A dimensional constant|
|unit is ms-2||unit is Nm2kg-2|
Deduce the dimensional formula for workdone,pressure and density. [posted by boineelo ]
We know that workdone = force x distance
Therefore [work done] = [force] [distance]
but force = ma
So, putting all these together
Similarly, you can work out the dimensional formula for pressure and density as
Ashmeeta Bhattarai asked:
“What are limitations of principle of homogeneity of dimensional analysis?”
The dimensional analysis has the following limitations
- It fails while using it to derive a relation among physical quantities, if there are more than 3 unknown variables on which a given physical quantity depends
- It does not tell whether a given Physical quantity is a scalar or a vector.
- It does not tell us the value of constants involved
- It does not always tell us the exact FORM of a relation
- It cannot be used for deriving logarithmic, trigonometric or exponential relations
- A dimensionally correct equation may not always be the correct relation. (Because there are more than one physical quantity having the same dimensions)
Know some more? Write them as comments to this post