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Figure shows the rectangular plate of length L . Left half of plate has density d1 and right half of plate has density d2 .

Center of mass of left half plate is at geometrical center CL . Center of mass of right half plate is at geometrical center CR .

Let A be the equal area of left half and right half parts of plate. Let t be the uniform thickness of plate.

Let mand mR be the masses of left side and right side plate .

Let us consider x-axis of x-y coordinate system be on the line joining the points od centre of massses  CL and CR .

Let Origin be the left edge of the full plate as shown in figure .

X-cooordinate X of centre of mass of full plate of length L is determined as

[ mL+ mR ] X  = mL × (L/4) + mR × (3L/4)  ......................... (1)

mass of plates are

mL = A × t × d1 ............................(2)

mR = A × t × d2 .........................(3)

By substituting the masses from eqn.(2) and eqn.(3) , we rewrite eqn.(1) after simplification as

[ d1 + d2 ] X   =  (L/4) ( d1 + 3 d2 )

X-cooordinate X of centre of mass of full plate of length L is

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