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Eight solid uniform cubes of edge l are ...

Eight solid uniform cubes of edge `l` are stacked together to form a single cube with centre `O`. One cube is removed from this system. Distance, of the centre of mass of remaining `7` cubes from `O` is.
.

A

`(7sqrt(3)l)/(16)`

B

`(sqrt(3))/(16)l`

C

`(sqrt(3))/(14)l`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
C
`7m(xhat(i)+yhat(j)+zhat(k))=M((l)/(2)hat(i)+(l)/(2)hat(j)+(l)/(2)hat(j))`
Shifting `=sqrt(x^(2)+y^(2)+z^(2))=sqrt(3),(l)/(sqrt(14))`
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Knowledge Check

  • Eight solid uniform cubes of edge l are stacked together to form a singlwe cube with centre O . One cube is removed from this system. Distance, of the centre of mass of remaining 7 cubes from O is. .

    A
    `(7sqrt(3 )l)/(16)`
    B
    `(sqrt(3 )l)/(16)`
    C
    `(sqrt(3 )l)/(14)`
    D
    zero

  • The position of the centre of mass of a cube of uniform mass density will be at

    A
    the centre of one face
    B
    the centre of the interaction of diagonals of one face.
    C
    the geometric centre of the cube
    D
    the edge of a cube

  • Two cubes of edge 10 m each joined together to form a single cuboid. The ratio of the total surface area of one of the cubes and that of the single cuboid formed is ______.

    A
    `5:3`
    B
    `2:1`
    C
    `3:5`
    D
    `1:2`

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