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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
![Wale need to determine the moment of inertia,
(a). Given, y = 4-x ²₁ x=0, y = 0;
Firstly
of region A= SS dA
4-x²
5 gtx dydx
n
2.
we find the area
• Ix =
1yjo
jo 18).
4-x²
olz
1-0
(4-x²) dx
A = [4X-3³] → [A = 16
3
Now, moment of inestia about x-axis!
Ix=
2
SS y²dA =>
[² for x = y ² dy dz
4-x²
3 [ [²] dz 15 (64-x²_48x²7xx") dx
dx
усяке
y=0/2
1 [64x - 47-48.3² + 12 3² ] = 3 [126-128 - 128 +38²4 ]
3
-128+384
Now, about y-axis!
2
Ty - Sfelda = [t the "eldyde
= =)
Ix = 3 [- 2048 -] ²> Tx = 128 - 16 = x= 126 A
Ix
==
35
3
35
2
[²³x² [y]²x² dx => [² (²x²-x4) dx
=> y = (1) => y = —— A
Ty
: . Dy = [4 ²³-25] 2² = [ ²² - ³2²] = 64/²
15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bd81766-0103-4cb8-b3e9-5180278339b3%2Faf1920f9-e700-4d95-8e3b-7acf6b461476%2Fe70f62k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Wale need to determine the moment of inertia,
(a). Given, y = 4-x ²₁ x=0, y = 0;
Firstly
of region A= SS dA
4-x²
5 gtx dydx
n
2.
we find the area
• Ix =
1yjo
jo 18).
4-x²
olz
1-0
(4-x²) dx
A = [4X-3³] → [A = 16
3
Now, moment of inestia about x-axis!
Ix=
2
SS y²dA =>
[² for x = y ² dy dz
4-x²
3 [ [²] dz 15 (64-x²_48x²7xx") dx
dx
усяке
y=0/2
1 [64x - 47-48.3² + 12 3² ] = 3 [126-128 - 128 +38²4 ]
3
-128+384
Now, about y-axis!
2
Ty - Sfelda = [t the "eldyde
= =)
Ix = 3 [- 2048 -] ²> Tx = 128 - 16 = x= 126 A
Ix
==
35
3
35
2
[²³x² [y]²x² dx => [² (²x²-x4) dx
=> y = (1) => y = —— A
Ty
: . Dy = [4 ²³-25] 2² = [ ²² - ³2²] = 64/²
15
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