Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain

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#1

Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain.

Answer:

The dimensional formula for area a is given as follows:
image
Here, L is dimension of length.
The factor 2 is a constant, and it is dimensionless.
image That is dimension of area. When dimension is correct, dimension analysis cannot tell whether a constant like 2 should be there or not.
Thus, the dimensional analysis can not determine whether the area of a circle is πr2 or 2πr2 because the factor 2 is dimensionless.