Question

four point masses are placed at the corners of a square of side 2 m . find the centre of mass of the system w.r.t the centre of square.

Answer 1

we have to assume a square OABC of co-ordinates O =(0,0) , A = (2, 0) , B= (2, 2) and d = (0,2) as shown in figure.

now according to question, four point masses are placed at the corners of OABC square.
Let point masses of mass m are placed at four corner of square .

so, $C.M_x=\frac{m_1x_1+m_2x_2+m_3x_3+m_4x_4}{m_1+m_2+m_3+m_4}\\\\=\frac{m\times0+m\times2+m\times2+m\times0}{m+m+m+m}\\\\=\frac{2m+2m}{4m}\\\\=\frac{1}{2}$

similarly, $C.M_y=\frac{m_1y_1+m_2y_2+m_3y_3+m_4y_4}{m_1+m_2+m_3+m_4}\\\\=\frac{m\times0+m\times0+m\times2+m\times2}{m+m+m+m}\\\\=\frac{2m+2m}{4m}\\\\=\frac{1}{2}$

hence, CM = (1/2 , 1/2)

Answer 2

The question is incomplete. Here is the complete question:

Four point masses are placed at the corners of a square of side 2m. Find the center of mass of the system to the center of square. The masses of objects placed are 1kg,2kg,3kg and 4kg

Answer:

Let O is the center of the square.

A,B,C,D are the courses of the square.

A = 1kg

B = 2kg

C = 3kg

D = 4kg

The coordinates will be = (1,1)

B has coordinates = (-1,1)

C = (-1,-1)

D = (1,-1)

We know that it is being moved in the anti clockwise direction.

x base cm = m₁x₁ + m₂x₂ +m₃x₃ +m₄x₄ / m₁ +m₂ +m₃ +m₄

x base cm = 1-2-3+4 / 1 + 2 + 3 + 4 = 0

Now we will see the y coordinates of the center of mass:

y base cm = m₁y₁ + m₂y₂ +m₃y₃ +m₄y₄ / m₁ +m₂ +m₃ +m₄

y base cm = 1 +2 - 3 - 4/1 + 2 + 3 + 4 = -0.4

The coordinates will be = (0, - 0.4)