Find the Center of Mass of the Given System

question 80

Multiple Choice

Find the center of mass of the given system of point masses. $\begin{array}{|c|c|c|c|c|c|}\hline m_{i} & 8 & 8 & 8 & 7 & 9 \\\hline\left(x_{i}, y_{i}\right) & (5,-2) & (6,-7) & (2,4) & (-7,-7) & (-5,5) \\\hline\end{array}$

• A) \(\bar { x } = \frac { 13 } { 43 } , \bar { y } = - \frac { 41 } { 43 }\)
• B) \(\bar { x } = \frac { 9 } { 40 } , \bar { y } = - \frac { 9 } { 8 }\)
• C) \(\bar { x } = \frac { 1 } { 4 } , \bar { y } = - \frac { 11 } { 10 }\)
• D) \(\bar { x } = \frac { 13 } { 40 } , \bar { y } = - \frac { 41 } { 40 }\)
• E) \(\bar { x } = \frac { 3 } { 10 } , \bar { y } = - \frac { 21 } { 20 }\)

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Definitions:

Landscape Surface

The visible top layer of the earth's crust, including its physical features such as mountains, valleys, and plains.

Lithification

The conversion of unconsolidated sediment or volcanic ash into a coherent, solid rock, involving processes such as compaction and cementation.

Sedimentary Layers

Layers of rock or soil with internally consistent characteristics that distinguish them from contiguous layers.

Erosion

The method through which natural forces like wind or water cause the erosion and movement of soil, rock, and other materials on the surface.