Determine the Location of the Horizontal Axis $y _ { a }$

question 12

Multiple Choice

Determine the location of the horizontal axis $y _ { a }$ 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 $y _ { a } = \bar { y } - \frac { I _ { y } } { h A }$ where $\bar { y }$ is the $y$ -coordinate of the centroid of the gate, $I _ { y }$ 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)\(y _ { a } = - \frac { a ^ { 2 } } { L }\)
• B)\(y _ { a } = - \frac { 4 a ^ { 2 } } { 3 L }\)
• C)\(y _ { a } = - \frac { a ^ { 2 } } { 4 L }\)
• D)\(y _ { a } = - \frac { 5 a ^ { 2 } } { L }\)
• E)\(y _ { a } = - \frac { a ^ { 2 } } { 3 L }\)

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Definitions:

Upper Limb Length

The measurement from the top of the shoulder to the tip of the fingers, reflecting the dimensions of the arm and hand.

Body Height

The length of a human body from the bottom of the feet to the top of the head when standing upright.

Ratio

A ratio is a mathematical expression that compares two or more numbers, showing how much larger one quantity is than another.

Coefficient of Determination

This statistic measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model, often represented as R².