Determine the Location of the Horizontal Axis $y _ { a } \text { for figure (b) at which a vertical }$

question 108

Multiple Choice

Determine the location of the horizontal axis $y _ { a } \text { for figure (b) at which a vertical }$ gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a) ) . The model for $y _ { a }$ is $y _ { a } = \bar { y } - \frac { I _ { \bar { y } } } { h A }$ where $\bar { y }$ is the $y$ -coordinate of the centroid of the gate, $L _ { y }$ is the moment of inertia of the gate about the line $y = \bar { y } , h$ is the depth of the centroid below the surface, and $A$ is the area of the gate.

• A) \(y _ { a } = \frac { a ( 3 L - 2 a ) } { 2 ( 3 L + a ) }\)
• B)\(y _ { a } = \frac { 2 L } { 3 }\)
• C)\(y _ { a } = \frac { L } { 3 }\)
• D)\(y _ { a } = \frac { L } { 2 }\)
• E)\(y _ { a } = \frac { a ( 2 L + 3 a ) } { 3 ( 3 L - a ) }\)

---

Definitions:

Meaning In Life

Refers to the significance, purpose, or value one finds in their existence or in specific aspects of their life.

Autonomy

The capacity to make an informed, uncoerced decision or the state of being self-governing.

Competence

Refers to possessing the necessary abilities, knowledge, and skills to perform a task or job effectively and efficiently.

Maslow's Hierarchy

A theory in psychology proposed by Abraham Maslow, suggesting that people are motivated to achieve certain needs, which are arranged in a hierarchical order from physiological needs up to self-actualization.