Q 11-01-064JEE MainJEE Main 2026 (2 Apr, Shift 2)Medium
Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$, distance $(L)$, mass $(M)$ and time $(T)$ are ______.
Answer: (B) $[hT^{-1}LM^{-2}]$
$[G]=M^{-1}L^3T^{-2}$ and $[h]=ML^2T^{-1}$.
Four quantities but only three base dimensions, so check each option against $M^{-1}L^3T^{-2}$:
A: $hTLM^{-2}=(ML^2T^{-1})(T)(L)(M^{-2})=M^{-1}L^3T^{0}$ ✗
B: $hT^{-1}LM^{-2}=(ML^2T^{-1})(T^{-1})(L)(M^{-2})=M^{-1}L^3T^{-2}$ ✓
C: $hTL^2M^{-2}=M^{-1}L^4T^{0}$ ✗
D: $h^{-1}T^{-1}LM^{-2}=(M^{-1}L^{-2}T)(T^{-1})(L)(M^{-2})=M^{-3}L^{-1}T^{0}$ ✗
So $[G]=[hT^{-1}LM^{-2}]$.
Solution by Sreeraj P, M.Sc Physics