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.
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.
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.