Half of the recrtangular plate shown in figure is made of a material of density `rho_1` and the other half of density `rho_2`. The length of the plate is L. Locate the centre of mass of the plate.

Explanation

The centre of mass of each half is located at the geometricla centre of that half. Thus the left half may be replced by a pont particle of mss `Krho_1` placed at C_1` and the right half may be replaced by a point particle of mass `Krho_2` placed at `C_2`. This replacement is for the specific purpose of locatig the combined centre of mass. Take the middle point of the left edge to be the origin. The x-cordiN/Ate of the centre of mass is
`x=((Krho_1)L/4+(Krho_2)(3L)/3)/(Krho_1+Krho_2)`
`=(rho_1=3rho_2)/(4(rho_1+rho_2)) L`
the combined centre of mass is this much to the right of the assumed origin.