A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln(BD) holds true. Then which of the combination is not a meaningful quantity ?
Option 1)
Option 2)
Option 3)
Option 4)
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Hence![\left [ B.D \right ]= are \: dimensionless](https://learn.careers360.com/latex-image/?%5Cleft%20%5B%20B.D%20%5Cright%20%5D%3D%20are%20%5C%3A%20dimensionless)
&![\left [ A.D \right ]= \left [ C \right ]...............(2)](https://learn.careers360.com/latex-image/?%5Cleft%20%5B%20A.D%20%5Cright%20%5D%3D%20%5Cleft%20%5B%20C%20%5Cright%20%5D...............%282%29)
Relevent Concept here is :
Dimension -
The power to which fundamental quantities must be raised in order to express the given physical quantities.
-
Option 1)
Option 2)
Dimension of![\left [ A \right ]and \left [ C \right ]](https://learn.careers360.com/latex-image/?%5Cleft%20%5B%20A%20%5Cright%20%5Dand%20%5Cleft%20%5B%20C%20%5Cright%20%5D)
are not same hence its meaningless.
Option 3)
Since A D & C are of same dimension hence its meaningful.
Option 4)
Its meaningful.