Find the Moment of Inertia $I _ { y }$ Of the Lamina That Occupies the Region

question 174

Multiple Choice

Find the moment of inertia $I _ { y }$ 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 x-axis.

• A) \(\frac { 1 } { 24 }\)
• B) \(\frac { 1 } { 18 }\)
• C) \(\frac { 1 } { 12 }\)
• D) \(\frac { 1 } { 9 }\)
• E) \(\frac { 1 } { 6 }\)
• F) \(\frac { 1 } { 4 }\)
• G) \(\frac { 1 } { 3 }\)
• H) \(\frac { 1 } { 2 }\)

---

Definitions:

Inferior Rectus

A muscle in the eye that is responsible for downward eye movement.

Coracobrachialis

A muscle in the shoulder that assists in flexing and adducting the arm at the shoulder joint.

Pectoralis Major

A significant muscle located in the upper part of the chest that helps with shoulder and arm movements.

Deltoid

A sizable, three-sided muscle enveloping the shoulder joint tasked with raising the arm and providing the shoulder with its mobility.