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Half of the recrtangular plate shown in ...

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.

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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.
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