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A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.
- a)5
- b)10
- c)15
- d)20
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A rectangular block of dimensions 2 m × 1 m × 1 m is float...
Understanding Buoyancy
When a block floats in water, it displaces a volume of water equal to the weight of the block. The weight of the water displaced provides an upward buoyant force that balances the weight of the block.
Given Data
- Dimensions of the block: 2 m × 1 m × 1 m
- Immersed depth: 0.5 m
- Unit weight of water: 10 kN/m³
Calculating the Volume of Water Displaced
1. Calculate the volume of the submerged part of the block:
- The submerged volume (V) = Length × Width × Immersed Depth
- V = 2 m × 1 m × 0.5 m = 1 m³
2. Calculate the weight of the displaced water:
- Weight of displaced water (W_water) = Volume × Unit Weight of Water
- W_water = 1 m³ × 10 kN/m³ = 10 kN
Weight of the Block
According to Archimedes' principle, the weight of the block must equal the weight of the water displaced for it to float. Therefore, the weight of the block is:
- Weight of the block = Weight of the displaced water = 10 kN
Conclusion
Thus, the weight of the block is 10 kN, which corresponds to option B. This confirms that the buoyant force acting on the block equals its weight, allowing it to float.
When a block floats in water, it displaces a volume of water equal to the weight of the block. The weight of the water displaced provides an upward buoyant force that balances the weight of the block.
Given Data
- Dimensions of the block: 2 m × 1 m × 1 m
- Immersed depth: 0.5 m
- Unit weight of water: 10 kN/m³
Calculating the Volume of Water Displaced
1. Calculate the volume of the submerged part of the block:
- The submerged volume (V) = Length × Width × Immersed Depth
- V = 2 m × 1 m × 0.5 m = 1 m³
2. Calculate the weight of the displaced water:
- Weight of displaced water (W_water) = Volume × Unit Weight of Water
- W_water = 1 m³ × 10 kN/m³ = 10 kN
Weight of the Block
According to Archimedes' principle, the weight of the block must equal the weight of the water displaced for it to float. Therefore, the weight of the block is:
- Weight of the block = Weight of the displaced water = 10 kN
Conclusion
Thus, the weight of the block is 10 kN, which corresponds to option B. This confirms that the buoyant force acting on the block equals its weight, allowing it to float.
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A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct answer is option 'B'. Can you explain this answer?
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A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct 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 A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct 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 A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct answer is option 'B'. Can you explain this answer?.
A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct 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 A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct 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 A rectangular block of dimensions 2 m × 1 m × 1 m is floating in the water with immersing depth of 0.5 m. What is the weight of block (kN) if unit weight of water is 10 kN/cubic meter.a)5b)10c)15d)20Correct answer is option 'B'. Can you explain this answer?.
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