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Multivariable Calculus

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Center of Mass in Spherical Coordinates

MVCALC-AVEYKJ

Fin the center of mass (in spherical coordinates $(\rho, \theta,\varphi)$) for the lower half ball:

$$\{(\rho, \theta, \varphi): \rho\in[0, 2], \theta\in[0,2\pi], \varphi\in [\frac{\pi}{2}, \pi]\}$$

...with density $f(\rho, \theta, \varphi)=\frac{\rho+1}{2}.$

A

$(\frac{4}{5},0,0)$

B

$(0,0,\frac{4}{5})$

C

$(\frac{39}{50},0,0)$

D

$(0,0,\frac{39}{50})$

E

$(1,\pi,0)$