Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
Problem 35PQ
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Question
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Find dimensions of gravitational constant ‘G’
![Example 2: Find the dimensions of gravitational constant 'G’.
F = G
m,m,
Where symbols have their usual meaning.
Solution: From the given equation G =
F * r2
m,m2
Dimension of force [F] = [M][L][T²], dimension of [r] = [L²]
So the dimensions of [G]
[MLT [L]
3 [M'][L*][T²]
%3D
[M][M]
Example-3: Show that the equation
v = Vo + at
is dimensionally correct. Where symbols have their usual meaning.
Solution:
Dimension of LHS = [v] = [ LT]
Dimension of RHS = [ LT'] + [ LT²] [T]
= [LT'] +[LT'] = 2 [LT'] = [ LT']
of LHS = Dimension of RHS](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31a119a1-548b-46d6-9901-5b03277cd0ae%2F1d9f71e2-e3f6-41f5-8409-815562225963%2Fks0c78_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 2: Find the dimensions of gravitational constant 'G’.
F = G
m,m,
Where symbols have their usual meaning.
Solution: From the given equation G =
F * r2
m,m2
Dimension of force [F] = [M][L][T²], dimension of [r] = [L²]
So the dimensions of [G]
[MLT [L]
3 [M'][L*][T²]
%3D
[M][M]
Example-3: Show that the equation
v = Vo + at
is dimensionally correct. Where symbols have their usual meaning.
Solution:
Dimension of LHS = [v] = [ LT]
Dimension of RHS = [ LT'] + [ LT²] [T]
= [LT'] +[LT'] = 2 [LT'] = [ LT']
of LHS = Dimension of RHS
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Author:
Katz, Debora M.
Publisher:
Cengage Learning