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Dimensional Analysis

The velocity ...

Question

The velocity $v$ of a particle at time $t$ is given by $v = a t + \frac{b}{t + c}$ , where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are respectively

A

L T^{- 2}, L a n d T

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B

L^{- 2}, T a n d L T^{2}

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C

L T^{2}, L T a n d L

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D

L, L T a n d T^{2}

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Solution

The correct option is A $L T^{- 2}, L a n d T$

$[a] = [\begin{matrix} \frac{v}{t} \end{matrix}] = \frac{L T^{- 1}}{T} = L T^{- 2}, [C] = [t] = T$

$[b] = [v t] = L T^{- 1} T = L$

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