Question

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

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

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) = 1.1 \,m,\, 1.3\, m $