Question

Three point masses $M_1=1.6\text{kg},M_2=2.4\text{kg}$ and $M_3=2\text{kg}$ are placed at the corners of a thin massless rectangular sheet $(1.2\text{m}\times 1.0\text{m})$ as shown in the figure below. Centre of mass of the system will be located at a point (assuming $M_1$ to be at the origin)

• A. $(0.8,0.6)\text{m}$
• B. $(0.6,0.8)\text{m}$
• C. $(0.4,0.4)\text{m}$
• D. $(0.5,0.6)\text{m}$

Answer 1

The correct option is C $(0.4,0.4)\text{m}$

Given,
$\begin{array}{ccc}{x}_1=0\text{m}& y_1=0\text{m}& m_1=1.6\text{kg}\\ x_2=0\text{m}& y_2=1\text{m}& m_2=2.4\text{kg}\\ x_3=1.2\text{m}& y_3=0\text{m}& m_3=2.0\text{kg}\end{array}$

$x_{\text{cm}}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$
$=\frac{1.6\ast 0+2.4\ast 0+2\left(1.2\right)}{1.6+2.4+2}=0.4\text{m}$
$y_{\text{cm}}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$
$=\frac{1.6\ast 0+2.4\ast 1+2\left(0\right)}{1.6+2.4+2}=0.4\text{m}$
$\Rightarrow (x_{\text{cm}},y_{\text{cm}})=(0.4,0.4)\text{m}$