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}} $
