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Dimensional Analysis

A force F i...

Question

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

[M L T^{- 3}]

and

[M L T^{- 4}]

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[M L T^{- 3}]

and

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

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[M L T^{- 4}]

and

[M L T^{1}]

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[M L T^{- 3}]

and

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

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Solution

The correct option is A $[M L T^{- 3}]$ and $[M L T^{- 4}]$
From the principle of dimensional homogeneity
$[a] = [\frac{F}{t}] = [M L T^{- 3}]$
$[b] = [\frac{F}{t^{2}}] = [M L T^{- 4}]$

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