A ball is made of a material of density ρ, where ρ_oil < ρ < ρ_water with ρ_oil and ρ_water represent the densities of oil and water respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, the figure which represents the equilibrium position is :

1.

2.

3.

4.

A student is given three liquids A, B and C of densities ρ₁, ρ₂ and ρ₃. He has to arrange these liquids in order of their increasing densities. To do so, he takes an object and dips it in each liquid and observes that the object floats with 1/9, 2/11 and 3/7 parts of its volume outside the surface of liquid A, B and C respectively. The correct order is :

1. ρ₁ > ρ₂ > ρ₃
2. ρ₂ > ρ₃ > ρ₁
3. ρ₃ > ρ₂ > ρ₁
4. ρ₃ > ρ₁ > ρ₂

When a piece of wood is suspended from the hook of a spring balance, it reads 70 gf. The wood is now lowered into water. What reading do you expect on the scale of spring balance?

[Hint: The piece of wood will float on water and while floating, apparent weight = 0].

How does the density ρ_S of a substance determine whether a solid piece of that substance will float or sink in a given liquid of density ρ_L ?