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Physics · PYQ NEET UG 2017

हिन्दी

A physical quantity of the dimensions of length that can be formed out of \( c \), \( G \) and \( \frac{e^2}{4\pi\varepsilon_0} \) is [\( c \) is velocity of light, \( G \) is universal constant of gravitation and \( e \) is charge]:

  1. A
    \( \frac{1}{c^2}[G \frac{e^2}{4\pi\varepsilon_0}]^{1/2} \)
  2. B
    \( c^2[G \frac{e^2}{4\pi\varepsilon_0}]^{1/2} \)
  3. C
    \( \frac{1}{c^2}[\frac{e^2}{G 4\pi\varepsilon_0}]^{1/2} \)
  4. D
    \( \frac{1}{c}[G \frac{e^2}{4\pi\varepsilon_0}]^{1/2} \)
View Answer & Solution

Correct answer · Option A

\( \frac{1}{c^2}[G \frac{e^2}{4\pi\varepsilon_0}]^{1/2} \)

Explanation

Using dimensional analysis, length \( L \propto c^\alpha G^\beta (\frac{e^2}{4\pi\varepsilon_0})^\gamma \). Solving for the exponents gives \( L = \frac{1}{c^2} [ G \frac{e^2}{4\pi\varepsilon_0} ]^{1/2} \).
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