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A force $F$ is given by $F = a t + b t^{2}$ where $t$ is time, what are the dimension of $a$ and $b$ .

A. $M L T^{1}, M L T^{0},$

B. $M L T^{3}, M L^{2} T^{4},$

C. $M L T^{- 4}, M L T^{- 4},$

D. $M L^{- 3} T, M L T^{- 4},$

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Correct Answer :

D. $M L^{- 3} T, M L T^{- 4},$

a = \frac{F}{t} = M L T^{- 3}, b = \frac{F}{t^{2}} = M L T^{- 4}

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