Explanation:
It is given that,
Mass, [tex]m_1=4\ kg[/tex]
Center of gravity, [tex](x_1,y_1)=(0,0)[/tex]
Mass, [tex]m_2=3.2\ kg[/tex]
Center of gravity, [tex](x_2,y_2)=(0,6)[/tex]
Mass, [tex]m_3=1.4\ kg[/tex]
Center of gravity, [tex](x_3,y_3)=(4,0)[/tex]
Let the 6 kg object of mass is placed at point (x,y). The center of gravity is calculated as :
[tex]0=\dfrac{m_1x_1+m_2x_2+m_3x_3+m_4x_4}{m_1+m_2+m_3+m_4}[/tex]
[tex]0=\dfrac{4\times 0+3.2\times 0+1.4\times 4+6\times x}{4+3.2+1.4+6}[/tex]
x = -0.933 meters
For finding y,
[tex]0=\dfrac{m_1y_1+m_2y_2+m_3y_3+m_4y_4}{m_1+m_2+m_3+m_4}[/tex]
[tex]0=\dfrac{4\times 0+3.2\times 6+1.4\times 0+6\times y}{4+3.2+1.4+6}[/tex]
y = -3.2 meters
So, the center of gravity of the four-object arrangement will be at (-0.933,-3.2). Hence, this is the required solution.
