#### Density, Physics tutorial

Concept of density:

The density of the object refers to how heavy or light that object is relative to water or air. Density is stated as the mass of body per unit volume.

Density = Mass/Volume

That is, density of the body is mass of that body in kilograms per one meter cube of its volume

Thus to find out the density of the body, the given factors should be known: its mass and its volume.

Mass of the Body:

Quantity of matter in the body states its mass. It is a degree of inertia that is its reluctance to motion. It is estimated in kilogram (kg) using S.I. unit system. At times we use smaller units like (g) or milligram (mg).

Beam balance or scale may be utilized to estimate mass of the body. Mass of the body is compare with standard mass of one kilogram of Platinum-Iridium in Paris. Therefore by definition of density, find mass of object using beam balance.

Volume of a Body:

Volume of body is a amount of space it occupies - its capacity. It is estimated in cubic (m3) of cubic centimeter (cm3).

Volume of Regular Objects:

Regular objects comprise thing like cube, a cuboid, a cylinder, a sphere, and a cone. Their shapes are extremely different and unique. Their volume can then be determined with knowledge of their dimensions like height, length, breadth, radius or diameter.

Length, breadth and height of the cube are of same length l. Thus, by definition, volume of the cube.

V = l x l x l = l3.............Eq.1

1) Cuboid:

Cuboid has the height (h), breadth (b) and length (l). Therefore by definition volume of cuboid is

V = h x b x l.............Eq.2

2) Sphere:

The sphere is like the ball with the constant radius r or diameter D. BY definition, volume of the sphere is provided by

V = 4/3πr3.............Eq.3

Where, the diameter is provided as D, and where D = 2r

Therefore r = D/2

Therefore, in terms of diameter D volume of sphere can be stated as

V = 4/3π(D/2)3

V = 4/3πD3/8.............Eq.4

3) Cylinder:

The cylinder is like the drum or tin of milk with the height h and circular cross-section of radius r. By definition, volume of the cylinder is provided as

V = πr2h

This relation can also be stated in terms of Diameter D as

= π(D/2)3H

V = πD2/4h

4) Cone:

A cone is like the toy top with the circular surface that tapers to vertex. It is generally made from the sector of circular sheet. Vertical height of cone is h with circular base having the radius r. By definition volume of a cone is provided as

V = 4/3πr2h

Volume of Irregular Objects:

Irregular objects, in this case, are those objects which don't have regular shapes. The objects comprise stoned or any solid object which doesn't conform with any of regular objects. We employ indirect method of determining the volumes. Method is described as displacement method.

Density of Mixtures:

Mixtures of objects like alloys of metals or mixtures of liquids (water and alcohol). As different substances have different densities. Other mixtures will comprise acid solutions which is acid and water, water and milk etc. In science, there is generally the need to have such mixtures and therefore find out densities of such mixtures are helpful.

Assume there are given two substances A and B with the following properties:

Substance A

Mass of substance A = M1

Volume of substance A = V1

Density of substance A = ρ1

Substance B

Mass of substance B = M2

Volume of substance B = V2

Density of substance B = ρ2

Define the density of the mixture (ρ) if two substances are mixed together.

The density of the mixture can be represented as:

ρ = (Mass of A+ + mass of B)/(Volume of A + Volume of B)

In terms of the symbol

Therefore ρ = (M1 + M2)/(V1 + V2)

But M1 = ρ1V1 and M2 = ρ2V2

Therefore ρ = (ρ1V1 + ρ2V2) / (V1 + V2)

Therefore knowing values of ρ1, V1, ρ2 and V2, we are in the position to find out density of mixture ρ.

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