A) a b c \[[{{L}^{2}}]\] \[[T]\] \[[L{{T}^{2}}]\]
B) \[[L{{T}^{2}}]\] \[[LT]\] \[[L]\]
C) \[[L{{T}^{-2}}]\] \[[L]\] \[[T]\]
D) \[[L]\] \[[LT]\] \[[{{T}^{2}}]\]
Correct Answer: C
Solution :
\[v=at+\frac{\beta }{t+c}\] \[[at]=[v][L{{T}^{-1}}]\] \[\therefore \] \[[a]=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] Dimensions of\[c=[t][T]\] (we can add quantities of same dimensions only). \[\left[ \frac{b}{t+c} \right]=[v]=[L{{T}^{-1}}]\] \[[b]=[L{{T}^{-1}}][T][L]\]
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