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}} $



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