Question

The position of the centre of mass of the $\text{T}$ shaped plate from reference point $\text{O}$ as shown in the figure will be:

• A. $7.14\text{cm}$
• B. $5.28\text{cm}$
• C. $6.25\text{cm}$
• D. $4\text{cm}$

Answer 1

The correct option is B $5.28\text{cm}$

Divide the figure into $2$ rectangles $\text{ABCH}$ and $\text{DEGF}$ ,assigning the $x$ and $y$ axis:


Area of rectangle $\text{DEGF}$
$A_1=16{\text{cm}}^2$

Area of rectangle $\text{ABCH}$
$A_2=12{\text{cm}}^2$

Let us consider $c_1$ and $c_2$ to be the centres of mass of the two rectangles. Then,
coordinates of $c_1(x_1,y_1)=(0,7)$
coordinates of $c_2(x_2,y_2)=(0,3)$

To find the $\text{CM}$ of the $\text{T}$ shape, apply the formula by considering the $\text{CM's}$ of the individual rectangles and their areas.

$y_{\text{CM}}=\frac{A_1{y}_1+A_1{y}_2}{A_1+A_2}=\frac{(16\times 7)+(12\times 3)}{16+12}=\frac{148}{28}=5.28\text{cm}$

From the figure of $\text{T}$ shape, we can see that body is symmetrical about $y-$ axis, so the $\text{CM}$ of body will lie on the $y-$ axis only.
i.e $x_{\text{CM}}=0$

Hence, $\text{CM}$ of the $\text{T}$ shape will lie at a distance of $5.28\text{cm}$ from point $\text{O}$.