A) \[a\,\text{=}\,\text{ }\!\![\!\!\text{ }{{\text{L}}^{\text{2}}}\text{ }\!\!]\!\!\text{ ,}\,\text{b}\,\text{=}\,\text{ }\!\![\!\!\text{ T }\!\!]\!\!\text{ ,}\,\text{c}\,\text{=}\,\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{2}}}\text{ }\!\!]\!\!\text{ }\]
B) \[a\,\text{=}\,\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{2}}}\text{ }\!\!]\!\!\text{ ,}\,\text{b}\,\text{=}\,\text{ }\!\![\!\!\text{ LT }\!\!]\!\!\text{ ,}\,\text{c}\,\text{=}\,\text{ }\!\![\!\!\text{ L }\!\!]\!\!\text{ }\]
C) \[a\,\text{=}\,\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ ,}\,\text{b}\,\text{=}\,\text{ }\!\![\!\!\text{ L }\!\!]\!\!\text{ ,}\,\text{c}\,\text{=}\,\text{ }\!\![\!\!\text{ T }\!\!]\!\!\text{ }\]
D) \[a\,\text{=}\,\text{ }\!\![\!\!\text{ L }\!\!]\!\!\text{ ,}\,\text{b}\,\text{=}\,\text{ }\!\![\!\!\text{ LT }\!\!]\!\!\text{ ,}\,\text{c}\,\text{=}\,\text{ }\!\![\!\!\text{ }{{\text{T}}^{2}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: C
Solution :
\[v=at+\frac{b}{t+c}\] From principle of homogeneity of dimensions, Dimensions of at = dim of v \[\therefore \] Dimensions of a = dim of \[\frac{v}{t}\] \[=\frac{[L{{T}^{-1}}]}{[T]}=[L{{T}^{-2}}]\] Dimensions of c = dim of \[t=[T]\] Dimensions of \[\frac{b}{t}=\] dim of v Dimensions of b = dim of vt \[=[L{{T}^{-1}}]\times [T]=[L]\]
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