A) \[[L],\,[LT]\,\,and\,\,[L{{T}^{-\,2}}]\]
B) \[[L{{T}^{-\,2}}],\,\,[L]\,\,and\,\,[T]\]
C) \[[{{L}^{\,2}}],\,\,[T]\,\,and\,\,[L{{T}^{-\,2}}]\]
D) \[[L{{T}^{-\,2}}],\,[LT]\,and\,[L]\]
Correct Answer: B
Solution :
As, \[\operatorname{v}=\,\,at\,\,+\,\,\frac{b}{t+c}\] c can only be added to if it has same dimension at t, \[\therefore \,\,\,c=\left[ T \right]\] at must have dimension same as velocity i. e \[at=\left[ L{{T}^{-}}^{1} \right] \Rightarrow \, a =\,\,\frac{[L{{T}^{-\,1}}]}{[T]}\,\,=\,\,[L{{T}^{-}}^{2}]\]You need to login to perform this action.
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