A) \[{{[LT]}^{2}},[L]\]and [T]
B) \[[{{L}^{2}}],[T]\]and\[[L{{T}^{2}}]\]
C) \[[L{{T}^{2}}],[LT]\] and [L]
D) [L], [LT] and\[[{{T}^{2}}]\]
Correct Answer: B
Solution :
According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be the same. The given expression is \[v=at+\frac{b}{t+c}\] From principle of homogeneity \[[a][t]=[v]\] \[[a]=\frac{[v]}{[t]}=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] Similarly,\[[c]=[t]=[T]\] Further, \[\frac{[b]}{[t+c]}=[v]\] Or \[[b]=[v][t+c]\]or \[[b]=[L{{T}^{-1}}][T]=[L]\] Note: If a physical quantity depends on more than three factors, then relation among them cannot be established because we can have only three equations by equalising the powers of M, L and T.
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