Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)
$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$
A$(A,B,C)$
B$(A,B,D)$
C$(A,C,D)$
D$(B,C,D)$
IIT 2015, Diffcult
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C$(A,C,D)$
c $h \equiv\left[M^2 T^{-1}\right], c \equiv\left[L T^{-1}\right], G \equiv\left[M^{-1} L^3 T^{-2}\right] $
$M \propto \sqrt{\frac{h c}{G}}, L \propto \sqrt{\frac{h G}{c^3}}$
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