Verified answer

Given:

✰ Density of water = 4 kg/m³

✰ Density of ice = 2 kg/m³

✰ They are mixed together.

✰ Their masses are equal.

To find:

✠ The density of mixture.

Solution:

The density of a material is equal to its mass per unit volume. It's S.I. unit is kg/m³.

Here, in this question first we will find mass of water, then the mass of ice and then we will add both their masses and their volumes. After that we know that the density is equal to its mass per unit volume, so we will divide mass of both the substances by the volume of both to find the density of the mixture.

Let's find out...✧

✭ Density = Mass/Volume ✭

➛ Density of water = 4 kg/m³

➛ M/V₁ = 4

Here,

• M is the mass of water. ( Their masses are equal )
• V₁ is the volume of water.

➛ 4V₁ = M

➛ V₁ = M/4

➛ Density of ice = 2 kg/m³

➛ M/V₂ = 2 kg/m³

Here,

• M is the mass of ice. ( Their masses are equal )
• V₂ is the volume of ice.

➛ 2V₂ = M

➛ V₂ = M/2

Now,

➛ Density of mixture = Mass/Volume

➛ Density of mixture = (M + M)/(V₁ + V₂)

➛ Density of mixture = 2M/(M/4 + M/2)

➛ Density of mixture = 2M/((M + 2M)/4)

➛ Density of mixture = 2M/(3M/4)

➛ Density of mixture = 2M × 4/3M

➛ Density of mixture = 2M × 4/3M

➛ Density of mixture = 8M/3M

➛ Density of mixture ≈ 2.67 kg/m³

∴ The density of mixture ≈ 2.67 kg/m³

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