Three solid objects A, B, and C have the same volume but different masses. They are released gently, one by one, into tanks containing three different liquids:
L₁ (water), L₂ (kerosene) and L₃ (corrcentrated salt solution).

The observations made are as follows:

• Object A floats in L₁ and L₃ but sinks in L₂.
• Object B sinks in L₁, floats fully submerged in L₃, and sinks faster in L₂.
• Object C floats in all three liquids but with different heights submerged.

Answer the following:

(a) Arrange the liquids in increasing order of density, giving reasons.

(b) Identify the condition of flotation of object B in liquid L₃. What inference can be drawn about the densities of the object and liquid?

(c) "As object C floats in all three liquids, the upthrust acting on it is the same in all three cases." Is this statement correct? Explain.

(d) If object A is heated (without any change in mass) and then placed in L₁, what change, if any, will occur in its floating level?

(e) Two similar ships made of the same material float in fresh water and sea water respectively. Which ship displaces more water and why?

(a) From the observations :

• Object A sinks in L₂ but floats in L₁ and L₃, which means L₂ has the least density i.e., ρ_L2 < ρ_A < ρ_L1, ρ_L3.
• Object B sinks in L₁ but floats (fully submerged) in L₃, indicating that L₃ has the highest density i.e., ρ_L1 < ρ_B < ρ_L3.
• Since L₁ lies between these two cases, its density is intermediate.

Hence, the increasing order of density is ρ_L2 (kerosene) < ρ_L1 (water) < ρ_L3 (concentrated salt solution).

(b) The condition of flotation is:

W = F'_B

where,
W = weight of body acting vertically downwards
F'_B = Maximum upthrust that can act on the body

As object B floats fully submerged in L₃, hence, we can say that density of object B is equal density of liquid L₃

∴ ρ_object = ρ_L3

(c) The statement is correct because although object C floats in all three liquids, the upthrust acting on it is equal to its weight in each case, but the volume of liquid displaced is different depending on the density of the liquid.

In denser liquids, a smaller volume is displaced, while in less dense liquids, a larger volume is displaced so, while upthrust equals weight in all cases, the surrounding conditions like submerged volume differ.

(d) When object A is heated, its volume increases while its mass remains the same, leading to a decrease in its density so as a result, it will displace same amount of liquid to balance its weight but due to its larger volume it will be submerged less and hence will float higher in liquid L₁.

(e) The ship floating in fresh water displaces more volume because fresh water has lower density compared to sea water so to balance its weight, the ship must displace a larger volume of fresh water, whereas in denser sea water, a smaller volume is sufficient to provide the required upthrust.