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= 5. Find the x-coordinate of the center of mass of the thin flat plate of constant density 8 located in the first quadrant bounded from the top by y 1 and from 28 the bottom by y = x². You may use the fact that the mass M of the plate is

= 5. Find the x-coordinate of the center of mass of the thin flat plate of constant density 8 located in the first quadrant bounded from the top by y 1 and from 28 the bottom by y = x². You may use the fact that the mass M of the plate is

Advanced Engineering Mathematics
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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= 5. Find the x-coordinate of the center of mass of the thin flat plate of constant density & located in the first quadrant bounded from the top by y 1 and from 28 the bottom by y = x². You may use the fact that the mass M of the plate is 3
Transcribed Image Text:= 5. Find the x-coordinate of the center of mass of the thin flat plate of constant density & located in the first quadrant bounded from the top by y 1 and from 28 the bottom by y = x². You may use the fact that the mass M of the plate is 3
Expert Solution
Step 1: Introduction

We need to find the x minuscoordinate of the center of mass of the thin plate of constant density delta located in first quadrant bounded from the top by y equals 1 and from the bottom by y equals x squared.

The mass of the plate is M equals fraction numerator 2 delta over denominator 3 end fraction.

We know that the x minuscoordinate of center of mass is calculated as follows.

x with bar on top equals fraction numerator integral subscript R rho x d A over denominator integral subscript R rho d A end fraction, where rhois density, d A equals d y d x and Ris bounded region.

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