Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

A uniform object is formed by connecting three solid cubes with edge lengths $3\,\text{m}$, $2\,\text{m}$ and $1\,\text{m}$. The object has an axis of symmetry, and the cubes are arranged one above another with the cube of edge $2\,\text{m}$ positioned between the other two cubes (see diagram).
(i)[3]

Calculate the height of the centre of mass above the base of the largest cube.

(ii)[3]

The smallest cube is removed from the object and substituted with a heavier uniform cube of edge $1\,\text{m}$ made from a different material. The centre of mass of the object is then located at the base of the $2\,\text{m}$ cube. Find the ratio of the masses of the two cubes of edge $1\,\text{m}$.

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