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,

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Chapter1: Units, Trigonometry. And Vectors
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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 = xdmdm,ydmdm

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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