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

 

The x and y coordinates of the center of mass are given by:
x? = y? = 4a / 3π

From conservation of momentum:
2×4 = 2v? + mv?
Given v? = 1 m/s (interpreted from intermediate steps)
8 = 2 (1) + mv?
mv? = 6 . (i)
From coefficient of restitution (e=1 for elastic collision):
e = (v? - v? )/ (u? - u? )
1 = (v? - v? )/ (4 - 0)
-1 = (v? - v? )/ (0 - 4)  (as written in the image)
⇒ 4 =

$X_c=Y_c=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}=\frac{m\times 0+m\times 0+m\times 3}{3m}=1m$

$OC=X\sqrt[]{x_0^2+Y_c^2}=\sqrt[]{{\left(1\right)}^2+{\left(1\right)}^2}=\sqrt[]{2}m$

You should know that when the shift in the centre of mass occurs, you can use the principle of moments. With this logic, we can see the shift from the original body as the combination of two parts. The one that remains part and the other that is removed. The formula for the shift is the product of t

To study centre of mass, you need to follow these steps. 

• Learn the definition with examples. Most importantly, focus on visualising it. 
• Then approach the centre of mass formulas for discrete particles and continuous bodies.
• Practice finding the centre of mass for symmetrical and asymmetrica