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

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

Gravitation

Solution:

From $E=h v,[h] =\left[\frac{E}{v}\right]=\frac{ ML ^{2} T ^{-2}}{ T ^{-1}} $
$ = ML ^{2} T ^{-1} $
$F=\frac{G M m}{R^{2}},[G]=\left[\frac{F \cdot R^{2}}{ M \cdot m }\right]=\frac{ MLT ^{-2} \cdot L ^{2}}{ M ^{2}}= M ^{-1} \cdot L ^{3} \cdot T ^{-2}$
$[c]=L T^{-1} \Rightarrow \left[\frac{h c}{G}\right]=\frac{\left(M L^{2} T^{-1}\right) \cdot\left(L T^{-1}\right)}{M^{-1} L^{3} \cdot T^{-2}}=M^{2}$
The $SI$ unit of $\frac{h c}{G}$ is $kg ^{2}$