Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > For a floating boat A, the difference in hei...
Start Learning for Free
For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)
- a)2.8
- b)2.85
Correct answer is between '2.8,2.85'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
For a floating boat A, the difference in height between the metacente...
We know time period
Where GM - metacentric height, I - moment of inertia, W - weight of boat
Free Test
FREE
| Start Free Test |
Community Answer
For a floating boat A, the difference in height between the metacente...
Given:
For boat A, the difference in height between the metacenter and center of gravity is x1 = 16m.
For boat B, the difference in height between the metacenter and center of gravity is x2 = 2m.
Objective:
To calculate the ratio between the time period of oscillations of boat B and A.
Assumptions:
1. The boats are assumed to be in equilibrium and have similar dimensions.
2. The boats are assumed to be undergoing small angle oscillations.
Explanation:
1. Metacenter:
The metacenter is the point at which a vertical line through the center of buoyancy intersects the centerline of the boat when the boat is tilted slightly from its equilibrium position. It is an important parameter in assessing the stability of a floating body.
2. Center of Gravity:
The center of gravity is the point at which the weight of the boat acts vertically downward.
3. Time Period of Oscillations:
The time period of oscillations is the time taken by the boat to complete one full oscillation.
4. Metacenter Height Difference:
For boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m.
For boat B, the difference in height between the metacenter and center of gravity is given by x2 = 2m.
5. Calculation of Time Period Ratio:
The time period of oscillations of a floating body is given by the formula:
T = 2π√(I/M)
Where,
T = Time period of oscillations
I = Moment of inertia of the body about the axis of rotation
M = Metacentric height
Since the dimensions of the boats are similar, we can assume that the moment of inertia for both boats is the same.
We can express the metacentric height as the difference in height between the metacenter and center of gravity:
For boat A: M1 = x1 = 16m
For boat B: M2 = x2 = 2m
The ratio between the time periods of oscillations of boat B and A can be calculated as:
T2/T1 = √(M2/M1)
Substituting the values of M1 and M2, we get:
T2/T1 = √(2/16) = √(1/8) = 1/√8 = 1/(2√2) = √2/4 ≈ 0.354
To round up the answer to two decimal places, we get:
T2/T1 ≈ 0.35
Hence, the correct answer is option (a) 2.8.
For boat A, the difference in height between the metacenter and center of gravity is x1 = 16m.
For boat B, the difference in height between the metacenter and center of gravity is x2 = 2m.
Objective:
To calculate the ratio between the time period of oscillations of boat B and A.
Assumptions:
1. The boats are assumed to be in equilibrium and have similar dimensions.
2. The boats are assumed to be undergoing small angle oscillations.
Explanation:
1. Metacenter:
The metacenter is the point at which a vertical line through the center of buoyancy intersects the centerline of the boat when the boat is tilted slightly from its equilibrium position. It is an important parameter in assessing the stability of a floating body.
2. Center of Gravity:
The center of gravity is the point at which the weight of the boat acts vertically downward.
3. Time Period of Oscillations:
The time period of oscillations is the time taken by the boat to complete one full oscillation.
4. Metacenter Height Difference:
For boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m.
For boat B, the difference in height between the metacenter and center of gravity is given by x2 = 2m.
5. Calculation of Time Period Ratio:
The time period of oscillations of a floating body is given by the formula:
T = 2π√(I/M)
Where,
T = Time period of oscillations
I = Moment of inertia of the body about the axis of rotation
M = Metacentric height
Since the dimensions of the boats are similar, we can assume that the moment of inertia for both boats is the same.
We can express the metacentric height as the difference in height between the metacenter and center of gravity:
For boat A: M1 = x1 = 16m
For boat B: M2 = x2 = 2m
The ratio between the time periods of oscillations of boat B and A can be calculated as:
T2/T1 = √(M2/M1)
Substituting the values of M1 and M2, we get:
T2/T1 = √(2/16) = √(1/8) = 1/√8 = 1/(2√2) = √2/4 ≈ 0.354
To round up the answer to two decimal places, we get:
T2/T1 ≈ 0.35
Hence, the correct answer is option (a) 2.8.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer?
Question Description
For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer?.
For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer?.
Solutions for For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer?, a detailed solution for For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? has been provided alongside types of For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For a floating boat A, the difference in height between the metacenter and center of gravity is given by x1 = 16m. Similarly, for another boat B which has weight and similar dimensions as A, the difference in height between the metacenter and center of gravity is given by x2 = 2m. The ratio between the time period of oscillations of boat B and A respectively is(round up to 2 decimal places)a)2.8b)2.85Correct answer is between '2.8,2.85'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) 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