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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