Find the y-coordinate of the center of mass of the lamina that occupies the region $D = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ and whose density function at any point is the distance from that point to the y-axis.
A) $\frac { 1 } { 6 }$

B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 2 }$
E)
$\frac { 2 } { 3 }$
F) $\frac { 3 } { 4 }$

G) $\frac { 5 } { 6 }$

H)1

Question

Find the y-coordinate of the center of mass of the lamina that occupies the region $D = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ and whose density function at any point is the distance from that point to the y-axis.
A) $\frac { 1 } { 6 }$

B) $\frac { 1 } { 4 }$ 
C) $\frac { 1 } { 3 }$ 
D) $\frac { 1 } { 2 }$ 
E)
$\frac { 2 } { 3 }$ 
F) $\frac { 3 } { 4 }$

G) $\frac { 5 } { 6 }$

H)1

Quizplus · Accepted Answer

The y-coordinate of the center of mass ($\bar{y}$) is not affected by the density function being the distance from the y-axis, so it is simply the average y-value in a uniform square from 0 to 1, which is $\frac{1}{2}$.

Find the Y-Coordinate of the Center of Mass of the Lamina