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Given $F = (a / t) + b t^{2}$ , where F denotes force and t time. The dimensions of a and b are respectively:

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$[M L T^{- 1}] a n d [M L T^{- 4}]$

$[L T^{- 1}] a n d [T^{- 2}]$

$[T] a n d [T^{- 2}]$

$[L T^{2}] a n d [T^{- 2}]$

answer is A.

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Detailed Solution

$[a] = [F t] = [M L T^{- 2}] \times [T] = [M L T^{- 1}]$

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

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