A) \[[L{{T}^{-2}}],\,[L]\] 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: A
Solution :
| Key Idea: According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same. |
| The given expression is |
| \[v=at+\frac{b}{t+c}\] |
| From principle of homogeneity |
| \[\left[ a \right]\text{ }\left[ t \right]=\left[ v \right]\] |
| \[[a]=\frac{[v]}{[t]}=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] |
| Similarly, \[[c]=[t]=[T]\] |
| Further, \[\frac{[b]}{[t+c]}=[v]\] |
| or \[\left[ b \right]=\left[ v \right]\text{ }\left[ t+c \right]\] |
| or \[\left[ b \right]=\left[ L{{T}^{-1}} \right]\left[ T \right]=\left[ L \right]\] |
| 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 equalizing the powers of M, L and T. |
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