Mechanical Engineering Exam > Mechanical Engineering Questions > A wooden block in the form of a rectangular p...
Start Learning for Free
A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cm
long, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the block
long, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the block
- a)6 cm
- b)2.3 cm
- c)1.3 cm
- d)2.8 cm
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A wooden block in the form of a rectangular prism float with its short...
Most Upvoted Answer
A wooden block in the form of a rectangular prism float with its short...
To calculate the position of the meta centre of the block, we need to understand the concept of metacentric height and its calculation. The metacentric height is the distance between the center of gravity of an object and its metacenter. The metacenter is the point of intersection of the vertical line passing through the center of buoyancy of the submerged object.
1. Identify the given dimensions:
- Length of the block (L) = 40 cm
- Width of the block (W) = 20 cm
- Depth of the block (D) = 15 cm
- Depth of immersion (d) = 12 cm
2. Calculate the center of buoyancy (CB):
The center of buoyancy can be calculated by dividing the total submerged volume by the total submerged area.
Submerged volume = (Length of immersion) * (Width of the block) * (Depth of the block)
Submerged area = (Width of the block) * (Depth of the block)
Therefore, the center of buoyancy (CB) = (Submerged volume) / (Submerged area)
3. Calculate the position of the meta center (M):
The position of the meta center can be calculated using the formula:
Metacentric height (GM) = (Moment of inertia about the center of gravity) / (Displaced volume)
The moment of inertia about the center of gravity can be calculated using the formula:
Moment of inertia = (1/12) * (Length of the block) * (Width of the block)^3
Displaced volume = (Length of the block) * (Width of the block) * (Depth of immersion)
Therefore, GM = (Moment of inertia) / (Displaced volume)
The position of the meta center (M) = (CB) + (GM)
4. Substitute the values and calculate:
- Submerged volume = 12 cm * 20 cm * 15 cm = 3600 cm^3
- Submerged area = 20 cm * 15 cm = 300 cm^2
- CB = 3600 cm^3 / 300 cm^2 = 12 cm
- Moment of inertia = (1/12) * 40 cm * (20 cm)^3 = 53333.33 cm^4
- Displaced volume = 40 cm * 20 cm * 12 cm = 9600 cm^3
- GM = 53333.33 cm^4 / 9600 cm^3 = 5.55 cm
- M = 12 cm + 5.55 cm = 17.55 cm
Therefore, the position of the meta center of the block is approximately 17.55 cm from the center of buoyancy. However, none of the given options match this result. It seems there might be an error or inconsistency in the provided answer options.
1. Identify the given dimensions:
- Length of the block (L) = 40 cm
- Width of the block (W) = 20 cm
- Depth of the block (D) = 15 cm
- Depth of immersion (d) = 12 cm
2. Calculate the center of buoyancy (CB):
The center of buoyancy can be calculated by dividing the total submerged volume by the total submerged area.
Submerged volume = (Length of immersion) * (Width of the block) * (Depth of the block)
Submerged area = (Width of the block) * (Depth of the block)
Therefore, the center of buoyancy (CB) = (Submerged volume) / (Submerged area)
3. Calculate the position of the meta center (M):
The position of the meta center can be calculated using the formula:
Metacentric height (GM) = (Moment of inertia about the center of gravity) / (Displaced volume)
The moment of inertia about the center of gravity can be calculated using the formula:
Moment of inertia = (1/12) * (Length of the block) * (Width of the block)^3
Displaced volume = (Length of the block) * (Width of the block) * (Depth of immersion)
Therefore, GM = (Moment of inertia) / (Displaced volume)
The position of the meta center (M) = (CB) + (GM)
4. Substitute the values and calculate:
- Submerged volume = 12 cm * 20 cm * 15 cm = 3600 cm^3
- Submerged area = 20 cm * 15 cm = 300 cm^2
- CB = 3600 cm^3 / 300 cm^2 = 12 cm
- Moment of inertia = (1/12) * 40 cm * (20 cm)^3 = 53333.33 cm^4
- Displaced volume = 40 cm * 20 cm * 12 cm = 9600 cm^3
- GM = 53333.33 cm^4 / 9600 cm^3 = 5.55 cm
- M = 12 cm + 5.55 cm = 17.55 cm
Therefore, the position of the meta center of the block is approximately 17.55 cm from the center of buoyancy. However, none of the given options match this result. It seems there might be an error or inconsistency in the provided answer options.
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
A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer?
Question Description
A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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 wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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 wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer?.
A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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 wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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 wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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 A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A wooden block in the form of a rectangular prism float with its shortest axis vert ical. The block is 40 cmlong, 20cm wide and 15 cm deep with a dept h of imersion of 12 cm. Calculate the position of the meta centre of the blocka)6 cmb)2.3 cmc)1.3 cmd)2.8 cmCorrect answer is option 'C'. 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