Planck's constant h , speed of light c and gravitational constant G are used to form a unit of l

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1.Units, Dimensions and Measurement

hard

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)

Solution

$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] $

$M \propto \sqrt{\frac{h c}{G}}, L \propto \sqrt{\frac{h G}{c^3}}$

Standard 11

Physics

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