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A doubt from Dimensional Analysis

What about the correctness about the relation,

st=u+0.5a(2t-1), both dimensionally or any other

 Prakash Adhikari asked

Answer

The equation refers to the displacement in the tth second and hence it should have the dimensions of speed; since it is the displacement in one second.

Under this consideration, the equation is dimensionally and otherwise correct.

Limitations of Homogenity

Paraser asked

“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

A problem from Dimensional Analysis

if force F us given in terms of timeT and distance X f=AsinCT +BcosDX then the dimensions of A/B is equal to

Limitations of Dimensional Analysis

Ashmeeta Bhattarai asked:

“What are limitations of principle of homogeneity of dimensional analysis?”

The dimensional analysis has the following limitations

  1. 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
  2. It does not tell whether a given Physical quantity is a scalar or a vector.
  3. It does not tell us the value of constants involved
  4. It does not always tell us the exact FORM of a relation
  5. It cannot be used for deriving logarithmic, trigonometric or exponential relations
  6. A dimensionally correct equation may not always be the correct relation. (Because there are more than one physical quantity having the same dimensions)

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