Find the center of mass of the given system of point masses. $\begin{array}{|c|c|c|c|}
\hline m_{i} & 9 & 4 & 7 \
\hline\left(x_{i}, y_{i}\right) & (-1,0) & (7,-3) & (1,-9) \
\hline
\end{array}$

A) $\bar { x } = \frac { 5 } { 4 } , \bar { y } = - \frac { 19 } { 5 }$
B) $\bar { x } = \frac { 13 } { 10 } , \bar { y } = - \frac { 15 } { 4 }$
C) $\bar { x } = \frac { 29 } { 23 } , \bar { y } = - \frac { 72 } { 23 }$
D) $\bar { x } = \frac { 29 } { 20 } , \bar { y } = - \frac { 18 } { 5 }$
E) $\bar { x } = \frac { 7 } { 5 } , \bar { y } = - \frac { 73 } { 20 }$

Question

Find the center of mass of the given system of point masses. $\begin{array}{|c|c|c|c|}
\hline m_{i} & 9 & 4 & 7 \
\hline\left(x_{i}, y_{i}\right) & (-1,0) & (7,-3) & (1,-9) \
\hline
\end{array}$

A) $\bar { x } = \frac { 5 } { 4 } , \bar { y } = - \frac { 19 } { 5 }$
B) $\bar { x } = \frac { 13 } { 10 } , \bar { y } = - \frac { 15 } { 4 }$
C) $\bar { x } = \frac { 29 } { 23 } , \bar { y } = - \frac { 72 } { 23 }$
D) $\bar { x } = \frac { 29 } { 20 } , \bar { y } = - \frac { 18 } { 5 }$
E) $\bar { x } = \frac { 7 } { 5 } , \bar { y } = - \frac { 73 } { 20 }$

Quizplus · Accepted Answer

Using the formula for the center of mass of a system of point masses,
$$\bar { x } = \frac { \sum m_{i} x_{i} } { \sum m_{i} }, \bar { y } = \frac { \sum m_{i} y_{i} } { \sum m_{i} }$$
we get
$$\bar { x } = \frac{9(-1)+4(7)+7(1)}{9+4+7}=\frac{13}{10}$$
and
$$\bar { y } = \frac{9(0)+4(-3)+7(-9)}{9+4+7}=-\frac{15}{4}$$
Therefore, the answer is B.

Find the Center of Mass of the Given System of Point