Find the center of mass(x,y,z) of the following structure of four identical 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

Ans. (3)
First we find the center 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 center 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`