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Dimensional Analysis

The displacem...

Question

The displacement of a particle moving along $x$ -axis with respect to time $t$ is $x = a t + b t^{2} - c t^{3}$ . The dimensions of $c$ are

[T^{- 3}]

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[L T^{- 2}]

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[L T^{- 3}]

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[L T^{3}]

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[L T^{2}]

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Solution

The correct option is C $[L T^{- 3}]$
The displacement of a particle moving along $x$ -axis with respect to time $t$
$x = a t + b t^{2} - c t^{3}$
Dimension of $c t^{3} =$ Dimension of $x$
$[{c t}^{3}] = [x]$
or $[c] = \frac{[L]}{[T^{3}]}$
Dimension of $c = [L T^{- 3}]$

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