Question

Find the co-ordinates of the centre of mass of the lamina, shown in figure.

• A. $(0.75,1.75)$
• B. $(0.75,1.5)$
• C. $(0.5,1.75)$
• D. $(0.5,1.5)$

Answer 1

The correct option is A $(0.75,1.75)$


As we can see from the figure, the lamina is divided into two parts and their COM will be at their centres as shown.
Therefore,
${\overrightarrow{r}}_{com}=\frac{A_1\times {\overrightarrow{r}}_{com,1}+A_2\times {\overrightarrow{r}}_{com,2}}{A_1+A_2}$
Here, ${\overrightarrow{r}}_{com}$ is the position vector of COM w.r.t origin ($0,0$)

$\Rightarrow {\overrightarrow{r}}_{\text{com}}=\frac{2\times (\frac{\hat{i}}{2}+\hat{j})+2\times (\hat{i}+\frac{5\hat{j}}{2})}{2+2}$
$\Rightarrow {\overrightarrow{r}}_{\text{com}}=\frac{3}{4}\hat{i}+\frac{7}{4}\hat{j}$

or $r_{com}=(0.75,1.75)$