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A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:
- a)0.5 W
- b)W
- c)2W
- d)3 W
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A cylindrical piece of cork weighting 'W' floats with its axis...
Ans. (d) Due to own weight of cylinder, it will float upto 1/4th of its height in liquid of relative density of 4. To make it float in neutral equilibrium, centre of gravity and centre of buoyancy must coincide, i.e. cylinder upto full height must get immersed.
For free floating: Weight (W) = Buoyancy force (i.e. weight of liquid equal to 1/4th volume cork) The vertically downward force exerted by anchoring would be weight of
liquid equal to 3/4th volume cork = 3W.
For free floating: Weight (W) = Buoyancy force (i.e. weight of liquid equal to 1/4th volume cork) The vertically downward force exerted by anchoring would be weight of
liquid equal to 3/4th volume cork = 3W.
Most Upvoted Answer
A cylindrical piece of cork weighting 'W' floats with its axis...
Given information:
- A cylindrical piece of cork weighs W
- It floats in a liquid of relative density 4 with its axis in a horizontal position
- By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical
To find:
- The vertically downward force exerted by anchoring
Solution:
1. When the cork is floating with its axis in a horizontal position, the buoyant force acting on it is equal to its weight.
2. Let the volume of the cork be V and its density be p. Then its weight can be expressed as W = Vp.
3. When the cork is made to float with its axis vertical, the buoyant force acting on it is equal to the weight of the liquid displaced by it. Since the relative density of the liquid is 4, the weight of the displaced liquid is 4 times the weight of the cork.
4. Let the weight of the displaced liquid be F. Then F = 4Vp.
5. To keep the cork in neutral equilibrium position, the anchoring force must balance the weight of the cork and the weight of the displaced liquid acting downwards, and the buoyant force acting upwards.
6. Therefore, the anchoring force can be expressed as F + W = 5Vp.
7. Substituting the value of F, we get anchoring force as 5Vp = 5W.
8. Therefore, the vertically downward force exerted by anchoring is 3W, as W is the weight of the cork and the anchoring force is 5W, the difference is 3W.
Answer: The vertically downward force exerted by anchoring would be 3W.
- A cylindrical piece of cork weighs W
- It floats in a liquid of relative density 4 with its axis in a horizontal position
- By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical
To find:
- The vertically downward force exerted by anchoring
Solution:
1. When the cork is floating with its axis in a horizontal position, the buoyant force acting on it is equal to its weight.
2. Let the volume of the cork be V and its density be p. Then its weight can be expressed as W = Vp.
3. When the cork is made to float with its axis vertical, the buoyant force acting on it is equal to the weight of the liquid displaced by it. Since the relative density of the liquid is 4, the weight of the displaced liquid is 4 times the weight of the cork.
4. Let the weight of the displaced liquid be F. Then F = 4Vp.
5. To keep the cork in neutral equilibrium position, the anchoring force must balance the weight of the cork and the weight of the displaced liquid acting downwards, and the buoyant force acting upwards.
6. Therefore, the anchoring force can be expressed as F + W = 5Vp.
7. Substituting the value of F, we get anchoring force as 5Vp = 5W.
8. Therefore, the vertically downward force exerted by anchoring is 3W, as W is the weight of the cork and the anchoring force is 5W, the difference is 3W.
Answer: The vertically downward force exerted by anchoring would be 3W.
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Community Answer
A cylindrical piece of cork weighting 'W' floats with its axis...
We know the relative density is the ratio of weight of object to the weight of equal volume of water. if this ratio is less than 1 then workpiece will sink. it should be less than 1.
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A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer?
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A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer?.
A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical piece of cork weighting 'W' floats with its axis in horizontal position in a liquid of relative density 4. By anchoring the bottom, the cork piece is made to float at neutral equilibrium position with its axis vertical. The vertically downward force exerted by anchoring would be:a)0.5 Wb)Wc)2Wd)3 WCorrect answer is option 'D'. Can you explain this answer?.
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