Find the Moment or Center of Mass of the Wire $x ^ { 2 } + y ^ { 2 } = 25$

question 155

Multiple Choice

Find the moment or center of mass of the wire, as indicated.
-Find the center of mass of a wire that lies along the first-quadrant portion of the circle $x ^ { 2 } + y ^ { 2 } = 25$ if the density of the wire is $\delta = \cos \theta$ .

• A) \(\bar { x } = \frac { 5 } { 2 } , \bar { y } = \frac { 5 } { 2 }\)
• B) \(\bar { x } = \frac { 10 } { \pi } , \bar { y } = \frac { 10 } { \pi }\)
• C) \(\bar { x } = \frac { 5 } { 4 } , \bar { y } = \frac { 5 } { 4 }\)
• D) \(\bar { x } = \frac { 5 } { 3 } , \bar { y } = \frac { 5 } { 3 }\)

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Definitions:

Alkanes

Hydrocarbons containing only single carbon-carbon bonds, characterized by their saturated nature.

O-H Stretch

A vibrational mode observed in infrared spectroscopy, characteristic of the stretching of the O-H bond in molecules, indicative of the presence of alcohols or water.

Alcohols

Organic compounds characterized by one or more hydroxyl (-OH) groups attached to a carbon atom.

IR Absorption

A technique in spectroscopy where molecules absorb infrared light, causing vibrational transitions, used to identify chemical compounds.