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6)3 in the first quadrant, bclow thc graph of y=x³, for 0<1<2. Find the center of mass of a thin plate of constant mass density 8,

6)3 in the first quadrant, bclow thc graph of y=x³, for 0<1<2. Find the center of mass of a thin plate of constant mass density 8,

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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6)3 in the first quadrant, bclow thc graph of y=x³, for 0<1<2. Find the center of mass of a thin plate of constant mass density 8,
Transcribed Image Text:6)3 in the first quadrant, bclow thc graph of y=x³, for 0<1<2. Find the center of mass of a thin plate of constant mass density 8,
Expert Solution
Step 1

Given the equation of the graph:

y=x3

The coordinates of center of mass of a body are given as:

Xcm, Ycm = ∫xdm∫dm,∫ydm∫dm

Now, let us evaluate Xcm first as follows:

Consider a vertical strip of plate of vertical length "y" and width "dx" at a distance x  from the origin, now the area of the strip is given as:

A = ydxbut, since given y = x3 we can write:A = x3dx

Now, Since given that the plate is of uniform mass density (b) we can say that:

dm = x3dx(b)

 

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