The masses $m _ { i }$ are located at the point $P _ { 1 }$ . Find the moments $M _ { x }$ and $M _ { y }$ and the center of mass of the system. $m _ { 1 } = 3 , m _ { 2 } = 7 , m _ { 3 } = 111$ ; $$P _ { 1 } ( 1,5 ) , P _ { 2 } ( 3 , - 2 ) , P _ { 3 } ( - 2 , - 1 )$$
A) $M _ { x } = 18 , M _ { y } = 44 , \left( \frac { 44 } { 21 } , \frac { 18 } { 21 } \right)$
B) $M _ { x } = 44 , M _ { y } = 18 , \left( \frac { 44 } { 21 } , \frac { 18 } { 21 } \right)$
C) $M _ { x } = 18 , M _ { y } = 44 , \left( \frac { 18 } { 21 } , \frac { 44 } { 21 } \right)$
D) $M _ { x } = 44 , M _ { y } = - 18 , \left( - \frac { 44 } { 21 } , \frac { 18 } { 21 } \right)$
E) $M _ { x } = - 44 , M _ { y } = 18 , \left( \frac { 44 } { 21 } , - \frac { 18 } { 21 } \right)$

Question

Quizplus · Accepted Answer

The moments are calculated as $M_x = \sum m_i y_i$ and $M_y = \sum m_i x_i$. For the given points and masses, $M_x = 3(5) + 7(-2) + 111(-1) = 44$ and $M_y = 3(1) + 7(3) + 111(-2) = 18$. The center of mass is $\left(\frac{M_y}{\sum m_i}, \frac{M_x}{\sum m_i}\right) = \left(\frac{44}{121}, \frac{18}{121}\right)$.

The Masses mim _ { i }mi​ Are Located at the Point

The Masses $m _ { i }$ Are Located at the Point