The density of the metal sphere is 2 times the density of the liquid as proved.
Net upward force acting on the metal sphere
The net upward force acting on the sphere as it is dropped into the liquid is calculated as follows;
F = σVg - ρVg
ma = σVg - ρVg
where;
- ρ is density of the liquid
- σ is the density of the metal
- a is acceleration of the metal
σV(a) = σVg - ρVg
σ(a) = σg - ρg
σ(g/2) = σg - ρg
g(σ/2) = g(σ - ρ)
σ/2 = σ - ρ
σ/2 - σ = - ρ
-σ/2 = - ρ
σ = 2ρ
Thus, the density of the metal sphere is 2 times the density of the liquid as proved.
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