Find the center of mass `(x,y,z)` of the following structure of four idential cubes if the length of each side of a 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)

Answer

(C )

Explanation

First we find the centre of mass of 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 the COM of each cube as a point particle:
`x_(COM) = (0.5 + 1.5 + 0.5 + 0.5)/(4) = 0.75 , y_(COM) = (0.5 + 0.5 + 1.5 + 0.5)/(4) = 0.75`
`z_(COM) = (0.5 + 0.5 + 0.5 + 1.5)/(4) = 0.75`