Dimensions of universal gravitational constant in terms of Planck's constant , distance , mass and time are [2026]

Question

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$ , distance $(L)$ , mass $(M)$ and time $(T)$ are ______. [2026]

Smart Achievers · Accepted Answer

(2)

$G = M^{- 1} L^{3} T^{- 2}$ $(T)$

$h = M L^{2} T^{- 1}$ $. . . (i i)$

$Dividing eq. (i) to eq. (ii)$

$\frac{G}{h} = \frac{M^{- 1} L^{3} T^{- 2}}{M L^{2} T^{- 1}}$

$G = M^{- 2} L T^{- 1} h^{1}$

Solution

Q.
Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$ , distance $(L)$ , mass $(M)$ and time $(T)$ are ______. [2026]

1 $[h T L M^{- 2}]$

2 $[h T^{- 1} L M^{- 2}]$

3 $[h T L^{2} M^{- 2}]$

4 $[h^{- 1} T^{- 1} L M^{- 2}]$

Ans.
(2)

$G = M^{- 1} L^{3} T^{- 2}$ $. . . (i)$

$h = M L^{2} T^{- 1}$ $. . . (i i)$

$Dividing eq. (i) to eq. (ii)$

$\frac{G}{h} = \frac{M^{- 1} L^{3} T^{- 2}}{M L^{2} T^{- 1}}$

$G = M^{- 2} L T^{- 1} h^{1}$

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Solution

Q. Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are ______. [2026]

1 [hTLM-2]

2 [hT-1LM-2]

3 [hTL2M-2]

4 [h-1T-1LM-2]

Ans. (2) G=M-1L3T-2 ...(i) h=ML2T-1 ...(ii) Dividing eq. (i) to eq. (ii) Gh=M-1L3T-2ML2T-1 G=M-2LT-1h1