Physics And Measurement Question 33
Question: If the constant of gravitation $ (G) $ , Planck’s constant $ (h) $ and the velocity of light $ (c) $ be chosen as fundamental units. The dimension of the radius of gyration is
[AMU (Eng.) 1999]
Options:
A) $ {{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}} $
B) $ {{h}^{1/2}}{{c}^{3/2}}{{G}^{1/2}} $
C) $ {{h}^{1/2}}{{c}^{-3/2}}{{G}^{-1/2}} $
D) $ {{h}^{-1/2}}{{c}^{-3/2}}{{G}^{1/2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let radius of gyration $ [k]\propto {{[h]}^{x}}{{[c]}^{y}}{{[G]}^{z}} $
By substituting the dimension of $ [k]=[L] $ , $ [h]=[ML^{2}{{T}^{-1}}],[c]=[L{{T}^{-1}}],[G]=[{{M}^{-1}}L^{3}{{T}^{-2}}] $ and by comparing the power of both sides we can get
$ x=1/2,y=-3/2,z=1/2 $
So dimension of radius of gyration are $ {{[h]}^{1/2}}{{[c]}^{-3/2}}{{[G]}^{1/2}} $
