Find the moment or center of mass of the wire, as indicated.
-Find the center of mass of a wire that lies along the semicircle $y = \sqrt { 36 - x ^ { 2 } }$ if the density of the wire is $\delta =$ $| \cos \theta |$.
A) $\bar { x } = 2 , \bar { y } = 2$
B) $\bar { x } = 0 , \bar { y } = 3$
C) $\bar { x } = 0 , \bar { y } = 2$
D) $\bar { x } = 3 , \bar { y } = 3$

Question

Quizplus · Accepted Answer

The center of mass $\bar{x}$ for a symmetric object along the y-axis is 0 due to symmetry. For $\bar{y}$, using the formula for the center of mass with the given density, the calculation considering the semicircle's shape and the density function $| \cos \theta |$ leads to $\bar{y} = 3$, making the correct answer $\bar{x} = 0, \bar{y} = 3$.

Find the Moment or Center of Mass of the Wire y=36−x2y = \sqrt { 36 - x ^ { 2 } }y=36−x2​

Find the Moment or Center of Mass of the Wire $y = \sqrt { 36 - x ^ { 2 } }$