Physics
The figure shows three identical solid cubes P, Q, and R of the same volume and material placed in three different liquids in identical vessels.
Answer the following :
(a) Arrange the liquids in increasing order of density.
(b) Identify the condition of flotation of cube R in liquid B. What information does this give about the densities of cube R and liquid B?
(c) Compare the upthrust acting on cubes P, Q, and R.
(d) If cube P is placed in liquid B, predict whether it will float higher, lower, or remain fully submerged. Give reason.
(e) Which liquid exerts the maximum buoyant force on a cube when it is fully immersed, and why?
Archimedes' Principle
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Answer
(a) From the figure :
- Cube P is half submerged in liquid A,
- Cube Q is 3/4 submerged in liquid C, and
- Cube R is fully submerged in liquid B.
For identical objects, a greater submerged portion indicates a lower density of the liquid. Thus, liquid B (fully submerged) has the least density, liquid C (3/4 submerged) has intermediate density and liquid A (half submerged) has the highest density.
Hence, increasing order of density is ρB < ρC < ρA.
(b) The condition of flotation is:
W = F'B
where,
W = weight of cube R acting vertically downwards
F'B = Maximum upthrust that can act on cube R
As cube R floats fully submerged in liquid B, hence, we can say that density of cube R is equal density of liquid B.
∴ ρcube R = ρB
(c) All three cubes are identical and floating, so the upthrust acting on each cube is equal to its weight and since their weights are the same, the upthrust on P, Q, and R is equal, even though the submerged volumes differ.
Hence, upthrust on P = Q = R.
(d) We know that Cube R floats fully submerged in liquid B. As all the cubes are identical, so cube P when placed in liquid B will also float fully submerged.
Therefore, cube P will remain fully submerged in liquid B.
(e) Liquid A exerts the maximum buoyant force on a cube when it is fully immersed.
Reason : When a cube is fully immersed, the buoyant force depends on the density of the liquid and the volume displaced and since all cubes have the same volume, the liquid with the highest density will exert the maximum buoyant force, because buoyant force is directly proportional to the density of the liquid.
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