If $x$ and $R$ stands for distance, then which of the following is dimensionally same as $\int \frac{R d x}{x^{2}}$ ?

- \frac{R^{2}}{x}

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R x

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\frac{R}{x}

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2 R x

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Solution

The correct option is C $\frac{R}{x}$
Given, $\int \frac{R d x}{x^{2}}$
$\Rightarrow [\int \frac{R d x}{x^{2}}] = \frac{[R] [x]}{[x^{2}]} = \frac{[R]}{[x]}$

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Similar questions

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Let x and a stand for distance. Is $\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a} s i n^{- 1} \frac{a}{x}$ dimensionally correct ?

\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}

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a

\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a} {sin}^{- 1} \frac{a}{x}

\int \frac{d x}{\sqrt{a^{2} - x^{n}}} = s i n^{- 1} \frac{x}{a}

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