Mechanical Engineering Exam > Mechanical Engineering Questions > For the stability of a floating body, under t...
Start Learning for Free
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?
- a)Metacentre should be below the centre of gravity.
- b)Metacentre should be above the centre of gravity.
- c)Metacentre and centre of gravity must lie on the same horizontal line.
- d)Metacentre and the centre of gravity must lie on the same vertical line.
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
For the stability of a floating body, under the influence of gravity a...
Concept:
The partially submerged body resembles the floating body, where the weight of the body is balanced by the buoyancy force acting in the upwards direction. The stability of the floating is governed by the metacenter of the floating body.
Metacenter is the point about which a body starts oscillating when the body is tilted by a small angle. It is the point where the line of action of buoyancy will meet the normal axis of the body when the body is given a small angular displacement.
The partially submerged body resembles the floating body, where the weight of the body is balanced by the buoyancy force acting in the upwards direction. The stability of the floating is governed by the metacenter of the floating body.
Metacenter is the point about which a body starts oscillating when the body is tilted by a small angle. It is the point where the line of action of buoyancy will meet the normal axis of the body when the body is given a small angular displacement.
Stable equilibrium: Metacenter is above the center of gravity of the body, then the disturbing couple is balanced by restoring the couple, the body will be in stable equilibrium.
Unstable equilibrium: Metacenter is below the center of gravity of the body, then the disturbing couple is supported by restoring the couple, the body will be in unstable equilibrium.
Neutral equilibrium: The metacenter and the center of gravity coincides at the same point, then the body is in neutral equilibrium.
Free Test
FREE
| Start Free Test |
Community Answer
For the stability of a floating body, under the influence of gravity a...
Explanation:
Stability of a Floating Body:
When a body is floating in a fluid, it is subjected to the forces of gravity and buoyancy. The stability of the floating body refers to its ability to return to its original position after being disturbed by an external force. The stability depends on the relative positions of the body's center of gravity and the metacentre.
Metacentre:
The metacentre (M) is the point of intersection of the vertical line passing through the buoyant force (B) and the vertical line passing through the center of gravity (G) of the floating body. It is a virtual point that helps in analyzing the stability of the floating body.
Center of Gravity:
The center of gravity (G) of a body is the point at which the entire weight of the body can be considered to act vertically downwards.
Stability Condition:
For a floating body to be stable under the influence of gravity alone, the metacentre should be above the center of gravity. This condition ensures that the restoring moment produced by the buoyant force is greater than the destabilizing moment produced by the weight of the body.
Explanation:
When the metacentre is above the center of gravity:
- Any small disturbance that causes the body to tilt will result in the center of buoyancy shifting to one side.
- As a result, a restoring moment is created due to the shift in the line of action of the buoyant force.
- This restoring moment tends to bring the body back to its original position, thus ensuring stability.
If the metacentre is below the center of gravity:
- Any small disturbance will cause the center of buoyancy to shift to one side.
- However, in this case, the restoring moment produced by the buoyant force is smaller than the destabilizing moment produced by the weight of the body.
- This leads to further tilting of the body, resulting in instability.
Therefore, the correct statement is option 'B': The metacentre should be above the center of gravity for the stability of a floating body under the influence of gravity alone.
Stability of a Floating Body:
When a body is floating in a fluid, it is subjected to the forces of gravity and buoyancy. The stability of the floating body refers to its ability to return to its original position after being disturbed by an external force. The stability depends on the relative positions of the body's center of gravity and the metacentre.
Metacentre:
The metacentre (M) is the point of intersection of the vertical line passing through the buoyant force (B) and the vertical line passing through the center of gravity (G) of the floating body. It is a virtual point that helps in analyzing the stability of the floating body.
Center of Gravity:
The center of gravity (G) of a body is the point at which the entire weight of the body can be considered to act vertically downwards.
Stability Condition:
For a floating body to be stable under the influence of gravity alone, the metacentre should be above the center of gravity. This condition ensures that the restoring moment produced by the buoyant force is greater than the destabilizing moment produced by the weight of the body.
Explanation:
When the metacentre is above the center of gravity:
- Any small disturbance that causes the body to tilt will result in the center of buoyancy shifting to one side.
- As a result, a restoring moment is created due to the shift in the line of action of the buoyant force.
- This restoring moment tends to bring the body back to its original position, thus ensuring stability.
If the metacentre is below the center of gravity:
- Any small disturbance will cause the center of buoyancy to shift to one side.
- However, in this case, the restoring moment produced by the buoyant force is smaller than the destabilizing moment produced by the weight of the body.
- This leads to further tilting of the body, resulting in instability.
Therefore, the correct statement is option 'B': The metacentre should be above the center of gravity for the stability of a floating body under the influence of gravity alone.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer?
Question Description
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. 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 For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. 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 For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer?.
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. 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 For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. 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 For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer?.
Solutions for For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?a)Metacentre should be below the centre of gravity.b)Metacentre should be above the centre of gravity.c)Metacentre and centre of gravity must lie on the same horizontal line.d)Metacentre and the centre of gravity must lie on the same vertical line.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup