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Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T…

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PYQ

Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are

[02 April, 2026 (Shift-2)]

\(\left[hTL{M}^{-2}\right]\)

\(\left[h{T}^{-1}L{M}^{-2}\right]\)

\([hT{L}^{2}{M}^{-2}]\)

\(\left[{h}^{-1}{T}^{-1}L{M}^{-2}\right]\)

✓ Correct answer: b)

\(\left[h{T}^{-1}L{M}^{-2}\right]\)

Explanation

Energy of a photon: \(E=\frac{hc}{\lambda }\)

Gravitational potential energy: \(E=\frac{G{M}_{1}{M}_{2}}{r}\)

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

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