Solutions
Concept-
Archimedes Principal
It states that when a body is partially or wholly immersed in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it and its upthrust acts through the center of the gravity of the displaced fluid.
Apparent weight of immersed body
The actual weight W of the immersed body acts downward and the upthrust U acts upwards.
∴ Apparent weight = Actual weight – Buoyant force
Wapp = W – U
Wapp = Vσ g – Vρ g = Vg(σ - ρ)
Where, V = volume of the liquid, σ = density of the body, ρ = density of the liquid and g = acceleration due to gravity.
Solution-
Consider a body of height h and density σ, lying inside a liquid of density ρ, at a depth x below the free surface of the liquid. Then the apparent weight of the immersed body is
Wapp = Vσg – Vρg = Vg(σ - ρ)
∴ The fraction of a ball floating inside the liquid depends upon both, the density of the liquid and density of the ball.