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Physics · PYQ NEET UG 2016(2)
हिन्दीPlanck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
Correct answer · Option 2
\( \frac{\sqrt{hG}}{c^{3/2}} \)
Explanation
Using dimensional analysis, \( [h] = ML^2T^{-1} \), \( [c] = LT^{-1} \), \( [G] = M^{-1}L^3T^{-2} \). Testing \( \sqrt{\frac{hc}{G}} \): \( \frac{(ML^2T^{-1})(LT^{-1})}{M^{-1}L^3T^{-2}} \) gives \( L^2 \), so square root gives \( L \) (length).
