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

question 117

Multiple Choice

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

---

Definitions:

Ecological

Relating to or concerned with the relation of living organisms to one another and to their physical surroundings.

Environment

The surroundings or conditions in which a person, plant, or animal lives or operates.

Kin-Work

The efforts and activities conducted by family members to maintain, support, and nurture their kinship networks and relationships.

Family Members

Individuals related by blood, marriage, or adoption who share a significant relational bond.