Find the Mass and Center of Mass of the Lamina $\rho = k$

question 101

Multiple Choice

Find the mass and center of mass of the lamina bounded by the graphs of the equations given below for the given density. $\rho = k$
$y = \sqrt { A ^ { 2 } - x ^ { 2 } } , y = 0$

• A) Mass \(= \frac { 1 } { 2 } A ^ { 2 } k , \bar { x } = 0 , \bar { y } = \frac { 4 A } { 3 \pi }\)
• B) Mass \(= \frac { 1 } { 2 } A ^ { 2 } k \pi , \bar { x } = 0 , \bar { y } = \frac { 4 A } { 3 }\)
• C) Mass \(= \frac { 1 } { 2 } A ^ { 2 } k \pi , \bar { x } = 0 , \bar { y } = \frac { 4 A } { 3 \pi }\)
• D) Mass \(= \frac { 1 } { 2 } A ^ { 2 } k \pi , \bar { x } = \frac { 4 A } { 3 \pi } , \bar { y } = \frac { 4 A } { 3 \pi }\)
• E) Mass \(= \frac { 1 } { 2 } A k \pi , \bar { x } = 0 , \bar { y } = \frac { 4 A } { 3 \pi }\)

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