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Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.
Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.
Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.
- a)Both A and R are individually true and R is the correct explanation ofA
- b)Both A and R are individually true but R is not the correct explanationof A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'A'. Can you explain this answer?
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Assertion (A): The buoyant force for a floating body passesthrough the...
Ans. (a) When a solid body is either wholly or partially immersed in a fluid, the hydrostatic lift due to net vertical component of the hydrostatic pressure forces experienced by the body is called the buoyant force. The buoyant force on a submerged or floating body is equal to the weight of liquid displaced by the body and acts vertically upward through the centroid of displaced volume known as centre of buoyancy.
The x coordinate of the center of the buoyancy is obtained as
Which is the centroid of the displaced volume. It is due to the buoyant force is equals to the weight of liquid displaced by the submerged body of volume and the force of buoyancy is a vertical force.
The x coordinate of the center of the buoyancy is obtained as
Which is the centroid of the displaced volume. It is due to the buoyant force is equals to the weight of liquid displaced by the submerged body of volume and the force of buoyancy is a vertical force.
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Assertion (A): The buoyant force for a floating body passesthrough the...
The statement is about the buoyant force acting on a floating body and its relationship with the centroid of the displaced volume.
To understand this, let's break down the statement and analyze each part separately.
Assertion (A): The buoyant force for a floating body passes through the centroid of the displaced volume.
The centroid of a shape is the point at which it would balance if it were supported at that point. In the case of a floating body, the buoyant force is the upward force exerted by a fluid on the body. This force is equal to the weight of the fluid displaced by the body.
Reason (R): The force of buoyancy is a vertical force equal to the weight of fluid displaced.
This reason is correct because the buoyant force is indeed a vertical force. It is equal to the weight of the fluid displaced by the body according to Archimedes' principle. When an object is immersed in a fluid, it experiences an upward buoyant force that is equal to the weight of the fluid it displaces.
Now let's analyze the relationship between the assertion and the reason.
The buoyant force acts in the upward direction and is equal to the weight of the fluid displaced. This force acts through the center of gravity of the displaced volume of fluid. The center of gravity of a regular shape, such as a cube or a sphere, coincides with its geometric center or centroid. However, for irregular shapes, the center of gravity may not coincide with the centroid.
In the case of a floating body, the buoyant force acts through the centroid of the displaced volume. This is because the buoyant force is distributed uniformly throughout the fluid, and the centroid represents the average location of this force distribution.
Therefore, both Assertion (A) and Reason (R) are individually true. Additionally, Reason (R) is the correct explanation of Assertion (A) because the buoyant force being a vertical force equal to the weight of fluid displaced explains why it passes through the centroid of the displaced volume.
Hence, the correct answer is option 'A' - Both A and R are individually true, and R is the correct explanation of A.
To understand this, let's break down the statement and analyze each part separately.
Assertion (A): The buoyant force for a floating body passes through the centroid of the displaced volume.
The centroid of a shape is the point at which it would balance if it were supported at that point. In the case of a floating body, the buoyant force is the upward force exerted by a fluid on the body. This force is equal to the weight of the fluid displaced by the body.
Reason (R): The force of buoyancy is a vertical force equal to the weight of fluid displaced.
This reason is correct because the buoyant force is indeed a vertical force. It is equal to the weight of the fluid displaced by the body according to Archimedes' principle. When an object is immersed in a fluid, it experiences an upward buoyant force that is equal to the weight of the fluid it displaces.
Now let's analyze the relationship between the assertion and the reason.
The buoyant force acts in the upward direction and is equal to the weight of the fluid displaced. This force acts through the center of gravity of the displaced volume of fluid. The center of gravity of a regular shape, such as a cube or a sphere, coincides with its geometric center or centroid. However, for irregular shapes, the center of gravity may not coincide with the centroid.
In the case of a floating body, the buoyant force acts through the centroid of the displaced volume. This is because the buoyant force is distributed uniformly throughout the fluid, and the centroid represents the average location of this force distribution.
Therefore, both Assertion (A) and Reason (R) are individually true. Additionally, Reason (R) is the correct explanation of Assertion (A) because the buoyant force being a vertical force equal to the weight of fluid displaced explains why it passes through the centroid of the displaced volume.
Hence, the correct answer is option 'A' - Both A and R are individually true, and R is the correct explanation of A.
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Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?
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Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. 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 Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. 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 Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?.
Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. 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 Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. 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 Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice Assertion (A): The buoyant force for a floating body passesthrough the centroid of the displaced volume.Reason (R): The force of buoyancy is a vertical force & equal tothe weight of fluid displaced.a)Both A and R are individually true and R is the correct explanation ofAb)Both A and R are individually true but R is not the correct explanationof Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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