Question

Three rods of the same mass are placed as shown in the figure. The co-ordinates of the centre of mass of the system is

• A. $(\frac{4}{3},2)$
• B. $(\frac{5}{3},2)$
• C. $(2,2)$
• D. $(1,\frac{1}{2})$

Answer 1

The correct option is A $(\frac{4}{3},2)$


As shown in figure, the centre of mass of the rods are at their respective mid points.
So, $(x_1,y_1)=(0,3)$, $(x_2,y_2)=(2,3)$, $\&(x_3,y_3)=(2,0)$

Let $x_{cm}$ and $y_{cm}$ be the co-ordinates of centre of mass of the system.
Then, $x_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$
$=\frac{m\left(0\right)+m\left(2\right)+m\left(2\right)}{3m}=\frac{4}{3}$
$y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$
$=\frac{m\left(3\right)+m\left(3\right)+m\left(0\right)}{3m}=2$
$(x_{cm},y_{cm})=(\frac{4}{3},2)$