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A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3?
Most Upvoted Answer
A cubical block is floating in a liquid with one fourth of its volume ...
The fraction of volume immersed in the liquid will be same as before i.e 1/2.
Fraction of volume immersed in the liquid
Vin=(ρ/σ)V
i.e. it depends upon the densities of the block and liquid. So there will be no change in it if system moves upward or downward with constant velocity or some acceleration.
Fraction of volume immersed in the liquid
Vin=(ρ/σ)V
i.e. it depends upon the densities of the block and liquid. So there will be no change in it if system moves upward or downward with constant velocity or some acceleration.
Community Answer
A cubical block is floating in a liquid with one fourth of its volume ...
The fraction of volume immersed in the liquid can be determined by considering the forces acting on the block and applying the principles of buoyancy.
1. Forces acting on the block:
- Weight (W) acting downwards: The weight of the block is given by W = mg, where m is the mass of the block and g is the acceleration due to gravity.
- Buoyant force (B) acting upwards: The buoyant force is equal to the weight of the liquid displaced by the block. It can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
2. Acceleration of the system:
The entire system, including the block and the liquid, is accelerating upwards with an acceleration of g/4.
3. Analysis of the forces:
- In the absence of acceleration, when the block is at rest, the weight of the block is balanced by the buoyant force, i.e., W = B.
- When the system accelerates upwards, the effective weight of the block (Weff) is given by Weff = W - B.
4. Calculation of the immersed volume:
Let the total volume of the block be V. Since one-fourth of the volume is immersed in the liquid, the volume immersed is V/4.
5. Solution:
- When the system accelerates upwards, the effective weight of the block is given by Weff = W - B.
- The weight of the block is W = mg.
- The buoyant force is B = ρgV/4, where ρ is the density of the liquid and V is the total volume of the block.
- Substituting the values, Weff = mg - ρgV/4.
- Since the system accelerates upwards with an acceleration of g/4, the effective weight becomes Weff = m(g - g/4).
- Simplifying, Weff = mg/4.
- Equating Weff to W - B, we get mg/4 = mg - ρgV/4.
- Simplifying further, V = 3/4.
- Therefore, the fraction of volume immersed in the liquid is 3/4.
Answer:
The fraction of volume immersed in the liquid is 3/4.
1. Forces acting on the block:
- Weight (W) acting downwards: The weight of the block is given by W = mg, where m is the mass of the block and g is the acceleration due to gravity.
- Buoyant force (B) acting upwards: The buoyant force is equal to the weight of the liquid displaced by the block. It can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
2. Acceleration of the system:
The entire system, including the block and the liquid, is accelerating upwards with an acceleration of g/4.
3. Analysis of the forces:
- In the absence of acceleration, when the block is at rest, the weight of the block is balanced by the buoyant force, i.e., W = B.
- When the system accelerates upwards, the effective weight of the block (Weff) is given by Weff = W - B.
4. Calculation of the immersed volume:
Let the total volume of the block be V. Since one-fourth of the volume is immersed in the liquid, the volume immersed is V/4.
5. Solution:
- When the system accelerates upwards, the effective weight of the block is given by Weff = W - B.
- The weight of the block is W = mg.
- The buoyant force is B = ρgV/4, where ρ is the density of the liquid and V is the total volume of the block.
- Substituting the values, Weff = mg - ρgV/4.
- Since the system accelerates upwards with an acceleration of g/4, the effective weight becomes Weff = m(g - g/4).
- Simplifying, Weff = mg/4.
- Equating Weff to W - B, we get mg/4 = mg - ρgV/4.
- Simplifying further, V = 3/4.
- Therefore, the fraction of volume immersed in the liquid is 3/4.
Answer:
The fraction of volume immersed in the liquid is 3/4.
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A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3?
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A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3?.
A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid.If whole of the system accelerates upward with acceleration g/4 , the fraction of volume immersed in the liquid will be (1)1/4 (2)1/2 (3)3/4 (4)2/3?.
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