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A thin rod of length L is placed along the x-axix with one end at the origin. If the density of the object varies linearly with x-that is, ? = ax2, where a is a positive constant-calculate the x-coordinate of the rod's center of mass. Express your answer in terms of a and L.
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COM_x = Integral (x dm) / Integral (dm)

Limits from 0 to L

density (rho)= ax^2

d(Mass) = (a x^2) * (dx) A

Integrating denominator

Mass = A * a * [L^3/3 - 0 ] = AaL^3 / 3

Integrating numerator (x * (a x^2) * (dx) A ) = A a [(L^4)/4 - 0 ] =AaL^4 / 4

So , X_com = (AaL^4 / 4) / (AaL^3 / 3) = 3L/4
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