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Center of Mass of a Wire

MVCALC-YXKE01

Let a wire takes the shape of the right semi-circle $x^2+y^2=1, x\geq 0$, the density of the wire is a linear function and is propositional to the distant from the position to the line $x=1$.

Find its center of mass.

A

$(0, 0)$

B

$(\frac{4-\pi}{2(\pi-2)}, 0)$

C

$(0, \frac{4-\pi}{2(\pi-2)})$

D

$(\frac{\pi}{4}, 0)$

E

Not enough information to determine