Dimensions: Practice Problem & Solution
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.
Solution Explained:
To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:
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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