Find the Center of Mass of a Thin Plate Covering $y = \frac { 8 } { x }$

question 254

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region between the curve $y = \frac { 8 } { x }$ and the $x$ -axis from $x = 1$ to $x = 9$ , with density $\delta ( x ) = \sqrt { x }$

• A) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 4 } { 3 }\)
• B) \(\bar { x } = 5 , \bar { y } = \frac { 8 } { 3 }\)
• C) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 128 } { 3 }\)
• D) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 8 } { 5 }\)

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Definitions:

Motor Units

The functional units of the neuromuscular system, consisting of a motor neuron and all the muscle fibers it innervates, responsible for muscle contraction.

Electromyography

A diagnostic procedure to assess the health of muscles and the nerve cells that control them, by measuring the electrical activity produced by muscles.

Skeletal

Relating to or constituting the bony framework of the body; involved in physical support and movement.

Motor Neuron

A type of neuron that transmits signals from the central nervous system to muscles or glands, resulting in movement or secretion.