A-LevelMathematicsMechanics9709/52 · Feb/Mar 2019 · Q26 Marks
A uniform object is made by joining together three solid cubes with edges 3m, 2m and 1m. The object has an axis of symmetry, with the cubes stacked vertically and the cube of edge 2 m between the other two cubes (see diagram).
- (i)Calculate the distance of the centre of mass of the object above the base of the largest cube.[3]
- (ii)The smallest cube is now removed from the object. It is replaced by a heavier uniform cube with 1 m edges which is made of a different material. The centre of mass of the object is now at the base of the 2 m cube. Find the ratio of the masses of the two cubes of edge 1 m.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B1] Total volume (= 27 + 8 + 1) = 36
- [M1] Take moments about base of largest cube
- 36x = 27×1.5+8×4+1×5.5
- [A1]
- x ( = 13/6) = 2.17 m
- [B1] Where m is the mass of the new cube
- Mass of new cube = 35+ m
- [M1] Take moments about base of largest cube
- (35 + m) × 3 =27×1.5 + 8×4 + 5.5m (leads to m = 13)
- [A1] Accept 13
- 13:1 or 1:13
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →