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A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:
- a)0.178 m
- b)0.250 m
- c)0.403 m
- d)0.500 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is wat...
Concept:
A wooden plank of W weight is floating on water as shown in figure.
The weight W and external load of 1.5 kN is acting downward and buoyancy force acts by water is in upward direction.
So by equating the forces, we will get, 1.5 + W = FB
Calculation:
Given:
Volume of plank V = 1 × 1 × 0.5 = 0.5 m3, Submerged volume Vs = 1 × 1 × h = h m3
So, from equation (1),
1.5 + (ρgV) = (ρgVs)
1.5 + (0.5 × 0.5 × 9.81) = 1 × h × 9.81
h = 0.4 m
Most Upvoted Answer
A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is wat...
Given data:
- Density of water = 1000 kg/m³
- Specific gravity of wooden plank = 0.5
- Load on the plank = 1.5 kN
- Dimensions of the plank: 1 m × 1 m × 0.5 m
Calculating the weight of the plank:
- Weight of the plank = Volume × Density × Specific gravity of wood
- Volume = 1 m × 1 m × 0.5 m = 0.5 m³
- Weight of the plank = 0.5 m³ × 1000 kg/m³ × 0.5 = 250 kg = 2.5 kN
Calculating the buoyant force acting on the plank:
- Buoyant force = Weight of water displaced = Weight of water × Volume displaced
- Weight of water displaced = Load on the plank + Weight of the plank
- Weight of water displaced = 1.5 kN + 2.5 kN = 4 kN
- Buoyant force = 4 kN
- Buoyant force = Weight of water × Volume displaced
- 4 kN = 1000 kg/m³ × 9.81 m/s² × Volume displaced
- Volume displaced = 0.407 m³
Calculating the depth of the plank below the water surface:
- Area of the plank in contact with water = 1 m × 1 m = 1 m²
- Volume displaced = Area of contact × Depth below water surface
- Depth below water surface = Volume displaced / Area of contact
- Depth below water surface = 0.407 m³ / 1 m² = 0.407 m ≈ 0.403 m
Therefore, the depth of the plank lying below the water surface is approximately 0.403 meters. So, the correct answer is option 'C'.
- Density of water = 1000 kg/m³
- Specific gravity of wooden plank = 0.5
- Load on the plank = 1.5 kN
- Dimensions of the plank: 1 m × 1 m × 0.5 m
Calculating the weight of the plank:
- Weight of the plank = Volume × Density × Specific gravity of wood
- Volume = 1 m × 1 m × 0.5 m = 0.5 m³
- Weight of the plank = 0.5 m³ × 1000 kg/m³ × 0.5 = 250 kg = 2.5 kN
Calculating the buoyant force acting on the plank:
- Buoyant force = Weight of water displaced = Weight of water × Volume displaced
- Weight of water displaced = Load on the plank + Weight of the plank
- Weight of water displaced = 1.5 kN + 2.5 kN = 4 kN
- Buoyant force = 4 kN
- Buoyant force = Weight of water × Volume displaced
- 4 kN = 1000 kg/m³ × 9.81 m/s² × Volume displaced
- Volume displaced = 0.407 m³
Calculating the depth of the plank below the water surface:
- Area of the plank in contact with water = 1 m × 1 m = 1 m²
- Volume displaced = Area of contact × Depth below water surface
- Depth below water surface = Volume displaced / Area of contact
- Depth below water surface = 0.407 m³ / 1 m² = 0.407 m ≈ 0.403 m
Therefore, the depth of the plank lying below the water surface is approximately 0.403 meters. So, the correct answer is option 'C'.
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A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer?
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A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? for EmSAT Achieve 2025 is part of EmSAT Achieve preparation. The Question and answers have been prepared according to the EmSAT Achieve exam syllabus. Information about A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for EmSAT Achieve 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer?.
A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? for EmSAT Achieve 2025 is part of EmSAT Achieve preparation. The Question and answers have been prepared according to the EmSAT Achieve exam syllabus. Information about A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for EmSAT Achieve 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer?.
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A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A wooden plank (sp.gr 0.5) 1 m × 1 m × 0.5 m floats is water with 1.5 kN load on it with 1 m × 1 m surface horizontal. The depth of plank lying below water surface shall be:a)0.178 mb)0.250 mc)0.403 md)0.500 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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