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MHT CET · Physics · Units and Dimensions

Which one of the following combination of constants has dimensions of time? \([\mathrm{G}=\) constant of gravitation, \(\mathrm{h}=\) Planck's constant, \(\mathrm{c}=\) velocity of light \(]\)

  1. A \(\left[\frac{G h}{c^{5}}\right]^{\frac{1}{2}}\)
  2. B \(\left[\frac{G h}{c}\right]^{\frac{1}{2}}\)
  3. C \(\left[\frac{G h}{c^{4}}\right]^{\frac{1}{2}}\)
  4. D \(\left[\frac{G h}{c^{3}}\right]^{\frac{1}{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left[\frac{G h}{c^{5}}\right]^{\frac{1}{2}}\)

Step-by-step Solution

Detailed explanation

\([G] = [M^{-1}L^3T^{-2}]\) \([h] = [ML^2T^{-1}]\)