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A force F is given by $F = a t + b t^{2}$ where ‘t’ is time. What are dimensions of ‘a’ and ‘b’?

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$M L T^{- 3} and M L^{2} T^{4}$

$M L T^{- 3} and M L T^{- 4}$

$M L T^{- 3} and M L T^{- 2}$

$M L T^{- 4} and M L T^{1}$

answer is B.

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Detailed Solution

According to homogeneity principle

(i) F=at

$a = \frac{F}{t} = \frac{M L T^{- 2}}{T^{1}} = M L T^{- 3}$

(ii) $F = b t^{2}$

$b = \frac{F}{t^{2}} = \frac{M L T^{- 2}}{T^{2}} = M L T^{- 4}$

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