Momentum and CollisionHard

Question

Find the center of mass (x,y,z) of the following stricture of four identical of four identical cubes if the length of each side of cube is 1 unit.

Options

A.(1 / 2, 1 / 2, 1 / 2)
B.(1 / 3, 1 / 3, 1 / 3)
C.(3 / 4, 3 / 4, 3 / 4)
D.(1 / 2, 3 / 4, 1 / 2)

Solution

First find the center of mass each cube, It is located by symmetry : (0.5, 0.5, 0.5), (1.5, 0.5, 0.5), (0.5, 1.5, 0.5), (0.5, 0.5, 1.5), Now we find the centre of mass by treating COM of each cube as a point particle :
xCOM = = 0.75 ; yCOM = = 0.75
zCOM = = 0.75

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