If $v = \frac{a}{t} + b t^{3}$ where, $v = velocity$ and $t$ is the time. The dimensional formula of $a$ and $b$ respectively are

[T], [T^{- 3}]

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

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[L^{- 1}], [L T^{- 3}]

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[L^{- 1}], [T^{- 3}]

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Solution

The correct option is B $[L], [L T^{- 4}]$
Given relation is $v = \frac{a}{t} + b t^{3}$
Using principle of dimensional homogeneity
$\Rightarrow [v] = [\frac{a}{t}] = [b t^{3}]$
$\Rightarrow [L T^{- 1}] = [a T^{- 1}] = [b T^{3}]$
$\Rightarrow [a] = [L]$ and $[b] = [L T^{- 4}]$

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