One of the combination from the fundamental physical constants is h c / G. The unit of this expression is

Question

One of the combination from the fundamental physical constants is h c / G. The unit of this expression is (A) kg 2 (B) m 3 (C) s -1 (D) none of the above

Tardigrade Admin · Accepted Answer

From E=h v,[h] =[(E/v)]=( ML 2 T -2/ T -1) = ML 2 T -1 F=(G M m/R2),[G]=[(F ⋅ R2/ M ⋅ m )]=( MLT -2 ⋅ L 2/ M 2)= M -1 ⋅ L 3 ⋅ T -2 [c]=L T-1 ⇒ [(h c/G)]=((M L2 T-1) ⋅(L T-1)/M-1 L3 ⋅ T-2)=M2 The SI unit of (h c/G) is kg 2

Q. One of the combination from the fundamental physical constants is h c / G. The unit of this expression is

$k g^{2}$

$m^{3}$

$s^{- 1}$

none of the above

Q. One of the combination from the fundamental physical constants is h c / G. The unit of this expression is

kg2

m3

s−1

none of the above

From E=hv,[h]=[vE​]=T−1ML2T−2​ =ML2T−1 F=R2GMm​,[G]=[M⋅mF⋅R2​]=M2MLT−2⋅L2​=M−1⋅L3⋅T−2 [c]=LT−1⇒[Ghc​]=M−1L3⋅T−2(ML2T−1)⋅(LT−1)​=M2 The SI unit of Ghc​ is kg2

$k g^{2}$

$m^{3}$

$s^{- 1}$