Question

Find the $x$ and $y$ -coordinates of the centre of mass of the three particle system (as shown).

• A. $1.0m,1.0m$
• B. $1.3m,0.9m$
• C. $1.1m,1.3m$
• D. $1.3m,1.1m$

Answer 1

Answer: (C)

Coordinates of centre of mass
$X_{CM}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$

$X_{CM}=\frac{0+8\times 1+4\times 2}{3+4+8}$
$=\frac{16}{15}$
$=1.1$
$Y_{CM}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$
$Y_{CM}=\frac{0+8\times 2+4\times 1}{3+4+8}$
$=\frac{20}{15}$
$=\frac{4}{3}=1.3$
$\left(X_{CM},Y_{CM}\right)=1.1m,1.3m$