Three cubes, of side L 0 , 2 L 0 , and 3 L 0 , are placed next to one another (i

Question

Three cubes, of side L0, 2L0, and 3L0, are placed next to one another (in contact) with their centers along a straight line as shown in (Figure 1) . What is the position, along the line

Three cubes, of side L0, 2L0, and 3L0, are placed next to one another (in contact) with their centers along a straight line as shown in (Figure 1) . What is the position, along the line x, of the CM of this system? Assume the cubes are made of the same uniform material and that xCM is measured from the left edge of the smallest cube

Explanation / Answer

CM of first will be at Lo/2

second will be at Lo+ 2Lo/2 = 2Lo

third cube CM will be at 3Lo + 3Lo/2 = 9Lo/2

Now going through basics of center of mass

Summation(Volume*CM) = net volume*netcm

Lo^3*Lo/2 + 8Lo^3*2Lo + 27Lo^3*4.5Lo = (27+8+1)Lo^3*x

Lo^4*(1/4 +16+ 243/2) = 36Lo^3x

x = 3.826Lo = Position of center of mass ,measuring from x=0

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