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A Uniform Wire Is Bent into a Semi-Circle of Radius π\pi

question 19

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A uniform wire is bent into a semi-circle of radius R and laid out such that it is entirely in the x-y plane .The semicircle has its ends fixed on the x axis at x = -R and x = +R.With the exception of its end points,the semicircle is entirely above the x-axis (i.e.the y-coordinates of all points on its arc are positive) .What is the y coordinate of its center-of-mass?

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Definitions:

Cerebral Cortex

The outer layer of the cerebrum composed of gray matter and consisting mainly of nerve cell bodies.

Alpha Rhythm

A pattern of smooth, regular electrical oscillations in the human brain typically occurring when a person is awake but relaxed, usually in the frequency range of 8-12 Hz.

Theta Rhythm

A pattern of brainwave activity, typically in the range of 4-8 Hz, associated with stages of sleep and meditative states.

Limbic System

In vertebrates, an action system of the brain. In humans, plays a role in emotional responses, motivation, sexual behavior, autonomic responses, and biological rhythms.

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