Question

Two identical uniform rods $\text{EF}$ and $\text{GH}$, each of length $L=6\text{cm}$ are joined as shown in figure. Locate the centre of mass of the frame.
[Point $\text{O}$, which is the point where the axes of the rods meet is the origin]

• A. $(0\text{m},0\text{m})$
• B. $(0\text{m},1\text{m})$
• C. $(0\text{m},1.5\text{m})$
• D. $(0\text{m},2\text{m})$

Answer 1

The correct option is C $(0\text{m},1.5\text{m})$

Let the masses of both rod $\text{EF}$ and $\text{GH}$ be $M\text{kg}$


Let the origin be at the point $\text{O}$. Then
$COM$ of rod $GH$, $\left(x_1{y}_1\right)=(0,0)$
$COM$ of rod $EF$, $\left(x_2{y}_2\right)=(0,3)$
Therefore,
$X$-coordinate of centre of mass of frame
$x_{com}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
$[\because m_1=m_2=M]$
$x_{com}=\frac{M\left(0\right)+M\left(0\right)}{M+M}=0\text{m}$
$Y$-coordinate of centre of mass of frame
$y_{com}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$
$y_{com}=\frac{M\left(0\right)+M\left(3\right)}{M+M}=\frac{3M}{2M}=\text{1.5 m}$
COM of the frame $(x_{com},y_{com})=(0\text{m},1.5\text{m})$