A circular plate of diameter d is placed in contact with a square plate of edge d , as shown in the figure. The density of the material and the thickness are uniform throughout. The centre of mass of the composite system will be located

Step-by-step solution

Let be the mass per unit area of the plates. Mass of the circular plate, M₁ = ( d 2 )^2 = d^2 4 Mass of the square plate, M₂ = d^2 Let the point of contact of the two plates be the origin (0,0) . The centre of mass of the circular plate is at x₁ = - d 2 . The centre of mass of the square plate is at x₂ = d 2 . The x -coordinate of the centre of mass of the composite system is given by: X_ cm = M₁ x₁ + M₂ x₂ M₁ + M₂ Substituting the values, we get: X_ cm = ( d^2 4 ) (- d 2 ) + ( d^2) ( d 2 ) d^2 4 + d^2 X_ cm = d 2