Ice at 0.0∘C has a density of 917 kg/m3. A 3.00 cm3 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, rhooil

When ice is neutrally buoyant, its weight equals to the buoyant force generated by the oil. Specifically, the weight of ice is the same as they weight of oil displaced by the volume of ice. Since they have the same volume, and same gravitational constant g anyway, this means the oil density must be at the same as ice's density, which is 917 kg/m3. As the formula for weight is

[tex]W = mg = \rhoVg[/tex]

Where [tex]\rho[/tex] is density, V is volume and g is the gravitational acceleration.

asuwafohjames asuwafohjames · Answer 2 · 2021-12-07T12:12:07+01:00

The density of the oil is 917 kg/m³

An object is said to be naturally buoyant , When it has the tendency to float in a fluid.

From the law of Floation, A floating body displaced an amount of fluid equal to its own weight.

That is,

Weight( W) = Upthrust (U)

W = U.......... Equation 1

Therefore,

U = DVg................. Equation 1

Where D = density of the ice, V = Volume of the ice, g = acceleration due to gravity.

From the question,

Given: D = 917 kg/m³, V = 3.00 cm³ = 3×10⁻⁶ m³, g = 9.8 m/s²

Substitute these values into equation 1

U = 917(3×10⁻⁶)(9.8)

U = 0.027 N

But,

Upthrust = weight of oil displaced.

And the ice will displaced an amount of oil, equal to its own weight.

Therefore,

Density of oil = U/gV = (0.027)/(3×10⁻⁶)(9.8)

Density of oil = 917 kg/m³

Hence the density of the oil is 917 kg/m³

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