GATE Exam > GATE Questions > A wooden block (relative density = 0.65) floa...
Start Learning for Free
A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface is
Correct answer is '0.519'. Can you explain this answer?
Verified Answer
A wooden block (relative density = 0.65) floats above surface of a liq...
Let V be total volume of wooden block and V’ is the volume that lies immersed in the liquid.
Using principle of floatation,
Weight of wooden block = weight of the liquid displaced by the immersed portion of the wooden block
So, the volume fraction of wooden block below the liquid surface = 1 – 0.4815 = 0.5185
Using principle of floatation,
Weight of wooden block = weight of the liquid displaced by the immersed portion of the wooden block
So, the volume fraction of wooden block below the liquid surface = 1 – 0.4815 = 0.5185
Most Upvoted Answer
A wooden block (relative density = 0.65) floats above surface of a liq...
Understanding the Problem
The problem involves a wooden block and a metallic piece floating in a liquid. We need to determine the volume fraction of the metallic piece that lies above the liquid surface.
Given Data
- Relative density of the wooden block = 0.65
- Relative density of the liquid = 1.35
Key Concepts
- Relative Density: The ratio of the density of a substance to the density of a reference substance (usually water).
- Buoyancy Principle: An object floats if its density is less than that of the liquid. The submerged part of the object displaces a volume of liquid equal to its weight.
Calculating Densities
- Density of wooden block = 0.65 * 1000 kg/m³ = 650 kg/m³
- Density of liquid = 1.35 * 1000 kg/m³ = 1350 kg/m³
Determining the Fraction Submerged
To find the volume fraction of the wooden block submerged in the liquid, use the concept of buoyancy:
- Volume submerged = Weight of the block / Density of the liquid
- Weight of the block = Volume of the block * Density of the block
Assuming the volume of the wooden block is V:
- Volume submerged = (V * 650) / 1350
- Ratio of submerged volume to total volume = 650 / 1350 = 0.481
Volume Above the Surface
The volume fraction of the wooden block above the liquid surface is:
- Volume above = 1 - Volume submerged = 1 - 0.481 = 0.519
Conclusion
Thus, the volume fraction of the metallic piece that lies above the liquid surface is 0.519. This means that approximately 51.9% of the block's volume is above the liquid surface, confirming the given answer.
The problem involves a wooden block and a metallic piece floating in a liquid. We need to determine the volume fraction of the metallic piece that lies above the liquid surface.
Given Data
- Relative density of the wooden block = 0.65
- Relative density of the liquid = 1.35
Key Concepts
- Relative Density: The ratio of the density of a substance to the density of a reference substance (usually water).
- Buoyancy Principle: An object floats if its density is less than that of the liquid. The submerged part of the object displaces a volume of liquid equal to its weight.
Calculating Densities
- Density of wooden block = 0.65 * 1000 kg/m³ = 650 kg/m³
- Density of liquid = 1.35 * 1000 kg/m³ = 1350 kg/m³
Determining the Fraction Submerged
To find the volume fraction of the wooden block submerged in the liquid, use the concept of buoyancy:
- Volume submerged = Weight of the block / Density of the liquid
- Weight of the block = Volume of the block * Density of the block
Assuming the volume of the wooden block is V:
- Volume submerged = (V * 650) / 1350
- Ratio of submerged volume to total volume = 650 / 1350 = 0.481
Volume Above the Surface
The volume fraction of the wooden block above the liquid surface is:
- Volume above = 1 - Volume submerged = 1 - 0.481 = 0.519
Conclusion
Thus, the volume fraction of the metallic piece that lies above the liquid surface is 0.519. This means that approximately 51.9% of the block's volume is above the liquid surface, confirming the given answer.
|
Explore Courses for GATE exam
|
|
Top Courses for GATEView all
Question Description
A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer?.
A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer?.
Solutions for A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer?, a detailed solution for A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? has been provided alongside types of A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface isCorrect answer is '0.519'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup