From the following combinations of physical constant (expressed… | JEE Main 2014 (12 Apr, Shift 1)

Q84JEE Main 2014 · 12 APR · SHIFT 1Medium

Units & Dimensions

From the following combinations of physical constant (expressed through their usual symbols) the only combination, that would have the same value in different systems of unit, is:

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Answer: (b)

A combination has the same value in every unit system only if it is dimensionless.
$\dfrac{e^2}{4\pi\varepsilon_0 r^2}$ and $\dfrac{G m_e^2}{r^2}$ are both forces.
So $\dfrac{e^2}{2\pi\varepsilon_0 G m_e^2} = 2\times\dfrac{e^2/(4\pi\varepsilon_0 r^2)}{G m_e^2/r^2}$ is dimensionless.
So the answer is (b).

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