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A body is floating as shown in the given figure. The centre of buoyancy, centre of gravity and metacentre are labelled respectively as B, G and M. The body is
- a)vertically stable
- b)vertically unstable
- c)rotationally stable
- d)rotationally unstable
Correct answer is option 'D'. Can you explain this answer?
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A body is floating as shown in the given figure. The centre of buoyanc...
Since metacentre is below centre of gravity the body is in unstable equilibrium in rotation.
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A body is floating as shown in the given figure. The centre of buoyanc...
Answer:
The given figure shows a body floating in a liquid. The centre of buoyancy, centre of gravity and metacentre are labelled as B, G and M respectively.
The body is rotationally unstable because of the following reasons:
1. Position of Centre of Gravity (G): The centre of gravity (G) of the body is below the centre of buoyancy (B). This means that the weight of the body acts downwards and creates a moment that tends to rotate the body. The farther the centre of gravity (G) is from the centre of buoyancy (B), the greater is the moment of rotation.
2. Metacentre (M) above Centre of Gravity (G): The metacentre (M) is located above the centre of gravity (G) of the body. Any disturbance that causes the body to tilt will cause the centre of buoyancy (B) to shift to a new position. The new position of centre of buoyancy (B) will create a moment that tends to rotate the body further. This moment will be proportional to the distance between the old and new positions of centre of buoyancy (B) and the weight of the displaced liquid.
3. Small Metacentric Height (GM): The metacentric height (GM) is the distance between the centre of gravity (G) and the metacentre (M). A small metacentric height (GM) indicates that the body is rotationally unstable. This is because any disturbance that causes the body to tilt will cause the centre of buoyancy (B) to shift to a new position. If the metacentric height (GM) is small, the moment created by the new position of centre of buoyancy (B) will be greater than the moment created by the weight of the displaced liquid. This will cause the body to rotate further and become unstable.
Therefore, the body is rotationally unstable because the position of centre of gravity (G) is below the centre of buoyancy (B), the metacentre (M) is above the centre of gravity (G), and the metacentric height (GM) is small.
The given figure shows a body floating in a liquid. The centre of buoyancy, centre of gravity and metacentre are labelled as B, G and M respectively.
The body is rotationally unstable because of the following reasons:
1. Position of Centre of Gravity (G): The centre of gravity (G) of the body is below the centre of buoyancy (B). This means that the weight of the body acts downwards and creates a moment that tends to rotate the body. The farther the centre of gravity (G) is from the centre of buoyancy (B), the greater is the moment of rotation.
2. Metacentre (M) above Centre of Gravity (G): The metacentre (M) is located above the centre of gravity (G) of the body. Any disturbance that causes the body to tilt will cause the centre of buoyancy (B) to shift to a new position. The new position of centre of buoyancy (B) will create a moment that tends to rotate the body further. This moment will be proportional to the distance between the old and new positions of centre of buoyancy (B) and the weight of the displaced liquid.
3. Small Metacentric Height (GM): The metacentric height (GM) is the distance between the centre of gravity (G) and the metacentre (M). A small metacentric height (GM) indicates that the body is rotationally unstable. This is because any disturbance that causes the body to tilt will cause the centre of buoyancy (B) to shift to a new position. If the metacentric height (GM) is small, the moment created by the new position of centre of buoyancy (B) will be greater than the moment created by the weight of the displaced liquid. This will cause the body to rotate further and become unstable.
Therefore, the body is rotationally unstable because the position of centre of gravity (G) is below the centre of buoyancy (B), the metacentre (M) is above the centre of gravity (G), and the metacentric height (GM) is small.
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A body is floating as shown in the given figure. The centre of buoyancy, centre of gravity and metacentre are labelled respectively as B, G and M. The body isa)vertically stableb)vertically unstablec)rotationally stabled)rotationally unstableCorrect answer is option 'D'. Can you explain this answer?
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