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Q.

With usual notation, amongst the following, the one which does not represent the dimensions of time is

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a

RC

b

$\sqrt{(LC)}$

c

L/R

d

$1 / \sqrt{(L / C)}$

answer is D.

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Detailed Solution

$[L] = [{ML}^{2} A^{- 2} T^{- 2}]$
$\begin{array}{l} [C] = \frac{[q]}{[V]} = \frac{[q^{2}]}{[W]} = \frac{[A^{2} T^{2}]}{[{ML}^{2} T^{- 2}]} \\ = [M^{- 1} L^{- 2} T^{4} Λ^{2}] \end{array}$
${[\sqrt{LC}] = \{[{ML}^{2} T^{- 2} A^{- 2}]\} \times [M^{- 1} L^{- 2} T^{4} A^{2}]\}}^{1 / 2}$
$= {[T^{2}]}^{1 / 2} = [T]$
$∴ \frac{1}{\sqrt{(LC)}} = [T^{- 1}]$

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