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Physics · UNITS AND MEASUREMENT
हिन्दीIf 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:
Correct answer · Option 1
\( [h^{1/2} G^{1/2} c^{-5/2}] \)
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 \( x = 1/2, y = 1/2, z = -5/2 \).
