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Physics · UNITS AND MEASUREMENT

हिन्दी

If Planck's constant (\( h \)), speed of light in vacuum (\( c \)), and Newton's gravitational constant (\( G \)) are taken as fundamental quantities, the dimension of time in terms of \( h \), \( c \), and \( G \) is:

  1. A
    \( [h^{1/2} G^{1/2} c^{-5/2}] \)
  2. B
    \( [h^{1/2} G^{1/2} c^{-3/2}] \)
  3. C
    \( [h^{1/2} G^{-1/2} c^{5/2}] \)
  4. D
    \( [h^{-1/2} G^{1/2} c^{3/2}] \)
View Answer & Solution

Correct answer · Option A

\( [h^{1/2} G^{1/2} c^{-5/2}] \)

Explanation

Let \( T = h^x G^y c^z \). Substituting dimensions \( [h] = [\text{M L}^2 \text{T}^{-1}] \), \( [G] = [\text{M}^{-1} \text{L}^3 \text{T}^{-2}] \), and \( [c] = [\text{L T}^{-1}] \) yields \( x = 1/2, y = 1/2, z = -5/2 \).
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