Physics And Measurement Question 123
Question: If the speed of light $ (c) $ , acceleration due to gravity $ (g) $ and pressure $ (p) $ are taken as the fundamental quantities, then the dimension of gravitational constant is
[AMU (Med.) 1999]
Options:
A) $ c^{2}g^{0}{{p}^{-2}} $
B) $ c^{0}g^{2}{{p}^{-1}} $
C) $ cg^{3}{{p}^{-2}} $
D) $ {{c}^{-1}}g^{0}{{p}^{-1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ [G]\propto c^{x}g^{y}p^{z} $
by substituting the following dimensions :
$ [G]=[{{M}^{-1}}L^{3}{{T}^{-2}}],[c]=[L{{T}^{-1}}],[g]=[L{{T}^{-2}}] $
$ [p]=[M{{L}^{-1}}{{T}^{-2}}] $
and by comparing the powers of both sides
we can get $ x=0,y=2,z=-1 $
$ ML^{2}{{T}^{-2}} $
$ [G]\propto c^{0}g^{2}{{p}^{-1}} $
