Solve the Problem $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 16 } { 5 } \frac { 1 } { \pi } \right)$

question 120

Multiple Choice

Solve the problem.
-Find the center of mass of the upper half of a solid ball of radius 3 centered at the origin if the density at any point is proportional to the distance from that point to the z-axis.

• A) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 16 } { 5 } \frac { 1 } { \pi } \right)\)
• B) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 3 } { 8 } ( 1 + \sqrt { 2 } ) \right)\)
• C) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 6 } { 5 } \right)\)
• D) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 3 } { 8 } \pi \right)\)

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