A-LevelMathematicsMechanics9709/51 · May/June 2017 · Q37 Marks
An object is made from a uniform solid hemisphere of radius 0.56m and centre O by removing a hemisphere of radius 0.28 m and centre O. The diagram shows a cross-section through O of the object.
- (i)Calculate the distance of the centre of mass of the object from O. [The volume of a hemisphere is ²⁄₃πr³.][4]
- (ii)The object has weight 24 N. A uniform hemisphere H of radius 0.28 m is placed in the hollow part of the object to create a non-uniform hemisphere with centre O. The centre of mass of the non-uniform hemisphere is 0.15 m from O. Calculate the weight of H.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] CofM of hemisphere = ³⁄₈ × 0.56 or ³⁄₈ × 0.28
- [M1A1] [²⁄₃π× 0.56³ - ²⁄₃π× 0.28³ ]X = ²⁄₃π× 0.56³ × ³⁄₈ × 0.56 - ²⁄₃π× 0.28³ × ³⁄₈ × 0.28
- [A1] X = 0.225 m
- [M1A1] 24 × 0.225 + W(3 × 0.28 / 8) = (24 + W) × 0.15
- [A1] W = 40 N
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