question_answer

A force F is given by \[F=at+b{{t}^{2}},\] where \[t\] is time, the dimensions of a and b are

A) \[[ML{{T}^{-3}}]\] and \[[ML{{T}^{-4}}]\]

B) \[[ML{{T}^{-3}}]\] and \[[M{{L}^{2}}{{T}^{-4}}]\]

C) \[[ML{{T}^{-4}}]\] and \[[ML{{T}^{1}}]\]

D) \[[ML{{T}^{-3}}]\] and \[[M{{L}^{2}}{{T}^{-4}}]\] From the principle of dimensional homogeneity \[[a]=\left[ \frac{F}{t} \right]=[ML{{T}^{-3}}]\] \[[b]=\left[ \frac{F}{{{t}^{2}}} \right]=[ML{{T}^{-4}}]\]