Question

Four particles of mass 2 Kg, 3 Kg, 5Kg and 2 Kg are situated at points A, B, C and D of square ABCD of side 1 meter respectively. Find the moment of inertia of the system about an axis through the centre of the square and perpendicular to the plane of the square.

Answer 1

To find centre of mass

$X_{COM}={\sum }_{i=1}^4{x}_1{M}_1$

$X_{COM}=\frac{M_i{x}_i+M_2{x}_2+M_3{x}_3+M_4{x}_4}{M_4+M_2+M_3+M_4}=\frac{0+0+3+4}{10}=\frac{7}{10}{Y}_{COM}={\sum }_{i=1}^4{Y}_i{M}_i=\frac{0+2+3+0}{10}=\frac{5}{10}=\frac{1}{2}(\frac{7}{10},\frac{1}{2})=COM$