**Problem 3:**(a) Use spherical coordinates to find the center of mass (CM) of a uniform solid hemisphere of radius \( R \), whose flat face lies in the \( xy \) plane with its center on the origin. *Note:* \( dV = r^2 \sin \theta \, dr \, d\theta \, d\phi. \)(b) Use your result from part (a) to calculate the CM of a hemispherical “bowl” with outer radius \( R \) and inner radius \( kR \), \( k < 1 \). (Depending on your work in part (a), you may not even need to do another integral.)(c) Use your result from the previous part to find the CM for an infinitely thin hemispherical shell of radius \( R \).

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Answered: Problem 3: (a) Use spherical…

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