Dimensional Analysis of Force Equation – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensional Analysis of Force Equation

In the given expression of force \(F = a log \left(\frac{b}{x}\right)\) where \(x\) is displacement, the dimensions of \(a\) and \(b\) respectively are
\([a] = [MLT^{-2}], [b] = [L]\)
\([a] = [M^{-1}], [b] = [L]\)
\([a] = [ML^{-1}], [b] = [MLT^{-1}]\)
\([a] = [MLT^{-2}], [b] = [ML^2]\)

Solution:

The argument of the logarithm must be dimensionless, so \([b] = [x] = [L]\). Since the logarithm term is dimensionless, \([a] = [F] = [MLT^{-2}]\).

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