Dimensions of Constants in Equation – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensions of Constants in Equation

Find dimensions of constants \(a\) & \(b\) in given equation: \(v = at^2\cos t + \frac{b}{t\sin\theta}\), where \(v \rightarrow\) velocity, \(t \rightarrow\) time.
\([LT^{-3}]\), \([L]\)
\([L^{-3}T]\), \([LT]\)
\([L^{-2}T]\), \([T]\)
\([LT^{-3}]\), \([LT]\)

Solution:

By the principle of homogeneity, each term on the right must have the dimensions of velocity \(v\). Thus, \([at^2] = [v] ⇒ [a] = [LT^{-3}]\), and \([\frac{b}{t}] = [v] ⇒ [b] = [L]\).

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