Physics And Measurement Question 138

Question: If the velocity of light $ (c) $ , gravitational constant $ (G) $ and Planck’s constant $ (h) $ are chosen as fundamental units, then the dimensions of mass in new system is

[UPSEAT 2002]

Options:

A) $ {{c}^{1/2}}{{G}^{1/2}}{{h}^{1/2}} $

B) $ {{c}^{1/2}}{{G}^{1/2}}{{h}^{-1/2}} $

C) $ {{c}^{1/2}}{{G}^{-1/2}}{{h}^{1/2}} $

D) $ {{c}^{-1/2}}{{G}^{1/2}}{{h}^{1/2}} $

Show Answer

Answer:

Correct Answer: C

Solution:

Let $ m\propto C^{x}G^{y}h^{z} $

By substituting the following dimensions: $ [C]=L{{T}^{-1}};[G]=[{{M}^{-1}}L^{3}{{T}^{-2}}] $

and $ [h]=[ML^{2}{{T}^{-1}}] $

Now comparing both sides we will get

$ x=1/2;y=-1/2,z=+1/2 $ So $ m\propto {{c}^{1/2}}{{G}^{-1/2}}{{h}^{1/2}} $



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