If the force is given by $F$ = $a t + b t^{2}$ with $t$ as time. The dimensions of a and b are:

[M L T^{- 4}], [M L T^{- 2}]

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[M L T^{- 3}], [M L T^{- 4}]

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[M L^{2} T^{- 3}], [M L^{2} T^{- 2}]

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[M L^{2} T^{- 3}], [M L^{3} T^{- 4}]

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Solution

The correct option is C $[M L T^{- 3}], [M L T^{- 4}]$
Dimension of force F : $[M L T^{- 2}]$
$F = a t + b t^{2}$
$⟹$ Dimension of $a : [M L T^{- 2}] \times [T^{- 1}]$ $= [M L T^{- 3}]$
Dimensions of $b : [M L T^{- 2}] \times [T^{- 2}]$ $= [M L T^{- 4}]$

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