Question

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $4\text{kg}$. (The coordinates of the same are shown in figure) are:

• A. $\text{1.25 m, 1.50 m}$
• B. $\text{0.75 m, 1.75 m}$
• C. $\text{0.75 m, 0.75 m}$
• D. $\text{1 m, 1.75 m}$

Answer 1

The correct option is B $\text{0.75 m, 1.75 m}$


The given Lamina can be divided into two parts, as shown.

The mass and the position of centre of mass of these parts are given by,

$m_1=1,C_1=(1.5,2.5)$
$m_2=3,C_2=(0.5,1.5)$
$X_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$\Rightarrow X_{cm}=\frac{1.5+1.5}{4}=0.75$
$Y_{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

$\Rightarrow Y_{cm}=\frac{2.5+4.5}{4}=1.75$

$\therefore$ Coordinate of the centre of mass of flag shaped lamina $(0.75,1.75)$

Hence, option $\left(B\right)$ is correct.