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The centre of gravity of a hemisphere lies at a distance of 3r / 8 from its base measured along the vertical radius.
- a)Correct
- b)Incorrect
Correct answer is option 'A'. Can you explain this answer?
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The centre of gravity of a hemisphere lies at a distance of 3r / 8 fro...
Explanation:
Centre of gravity is defined as the point where the whole weight of the object is supposed to be concentrated. In order to find the centre of gravity of a hemisphere, let's consider a hemisphere of radius 'r' as shown in the figure.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/2a50b25f6eaa6b40f8f7a4c91a1d3e06.png?height=200)
The centre of gravity of a hemisphere lies at a distance of 3r / 8 from its base measured along the vertical radius. Let's prove it.
- Consider a vertical plane passing through the centre of the hemisphere as shown in the figure.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/9a4e3b9b63b3a265d93b1d0e3d4a4d4d.png?height=200)
- The weight of the hemisphere acts through its centre of gravity 'G'. Let 'O' be the centre of the hemisphere.
- Let 'P' be the point where the weight of the hemisphere intersects the vertical radius 'OG'. The distance OP is equal to the radius 'r' of the hemisphere.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/83c00d6e2c9e1d5b8c9abc5c5dd9e3e4.png?height=200)
- Let 'x' be the distance between the centre of gravity 'G' and the point 'P'. Therefore, OG = (3/8)r + x.
- Let 'h' be the distance between the point 'P' and the base of the hemisphere. Therefore, h = r - x.
- The weight of the hemisphere acts through its centre of gravity 'G'. Therefore, the weight of the hemisphere is balanced by the weight of the hemisphere acting through the point 'P'.
- Consider a small element of volume 'dV' at a distance 'y' from the base of the hemisphere as shown in the figure.
[](https://d3j7fudf8hjnf2
Centre of gravity is defined as the point where the whole weight of the object is supposed to be concentrated. In order to find the centre of gravity of a hemisphere, let's consider a hemisphere of radius 'r' as shown in the figure.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/2a50b25f6eaa6b40f8f7a4c91a1d3e06.png?height=200)
The centre of gravity of a hemisphere lies at a distance of 3r / 8 from its base measured along the vertical radius. Let's prove it.
- Consider a vertical plane passing through the centre of the hemisphere as shown in the figure.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/9a4e3b9b63b3a265d93b1d0e3d4a4d4d.png?height=200)
- The weight of the hemisphere acts through its centre of gravity 'G'. Let 'O' be the centre of the hemisphere.
- Let 'P' be the point where the weight of the hemisphere intersects the vertical radius 'OG'. The distance OP is equal to the radius 'r' of the hemisphere.
[](https://d3j7fudf8hjnf2.cloudfront.net/image/resource/83c00d6e2c9e1d5b8c9abc5c5dd9e3e4.png?height=200)
- Let 'x' be the distance between the centre of gravity 'G' and the point 'P'. Therefore, OG = (3/8)r + x.
- Let 'h' be the distance between the point 'P' and the base of the hemisphere. Therefore, h = r - x.
- The weight of the hemisphere acts through its centre of gravity 'G'. Therefore, the weight of the hemisphere is balanced by the weight of the hemisphere acting through the point 'P'.
- Consider a small element of volume 'dV' at a distance 'y' from the base of the hemisphere as shown in the figure.
[](https://d3j7fudf8hjnf2
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The centre of gravity of a hemisphere lies at a distance of 3r / 8 from its base measured along the vertical radius.a)Correctb)IncorrectCorrect answer is option 'A'. Can you explain this answer?
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