JEE Main 2014 · 12 Apr · Shift 1 · Physics Q1

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

\dfrac{ch}{2\pi\epsilon_o^2}

\dfrac{e^2}{2\pi\epsilon_oGm_e^2}

(

m_e

= mass of electron)

\dfrac{\mu_o\epsilon_o}{c^2}\,\dfrac G{he^2}

\dfrac{2\pi\sqrt{\mu_o\epsilon_o}}{ce^2}\,\dfrac hG

Answer and worked solution

Official answer: B

A quantity has the same value in every system of units only if it is dimensionless.

$\dfrac{e^2}{4\pi\epsilon_o}$ has the dimensions of force × length², and so does $Gm_e^2$ . Their ratio $\dfrac{e^2}{2\pi\epsilon_oGm_e^2}$ is a pure number. The other three combinations all carry dimensions.

Topics:Dimensional analysis

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JEE Main 2014 · 12 Apr · Shift 1, Physics question 1