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Density typically means mass divisible by volume i.e. mass/volume. Thus, the unit of mass is kg and the unit of volume is meter3. Putting this into the mathematical equation, we get Density=kg/m3. However, here kg is the unit of mass and for dimension, we represent the mass by capital [M] and the same goes for the volume. Volume is basically the length so the unit of volume is meter cube which is denoted by capital [L]. Now putting caDerivationpital M and L in the above equation, the dimension formula of density is

**Density (ρ) = M1/L-3 T0**

Where,

M = Mass

L = Length

T = Time for Dimension of Density

Density refers to the mass per unit Volume

ρ=mass /Volume= M/V

Now, the Dimension of Mass = (M1)

Now, the Dimension of Volume = (L3)

Therefore, the Dimension of Density is given by

Dimension of Density= {M1} / {L3} = M1/ L-3

Unit of Density is kg/m3

We can find out the dimension of energy from the following equation.

E = Force x Displacement

Or, E= Mass x Acceleration x Displacement

Hence, putting the dimension of mass as [M], acceleration as [LT2] and the dimension of displacement as [L], we obtain the dimension of energy as [ML2 T-2]

Energy is the ability to perform an activity. Work, on the other hand, is defined as a force operating through a distance so the fundamental dimensional units of energy are force x distance. Based on what means of measurement you use, this could be dyne-centimetres, Newton-meters or foot-pounds. To measure energy, any combination of force and distance could be used. A couple of these units have specified names. A Newton-meter is described as a Joule. You see Joules most often on surge suppressors. A dyne-centimetre is described as an Erg (a unit of energy which is equivalent to 10 joules). There is also exercise equipment named Ergometer.

Energy comes in various forms and can thus be defined in special dimensional units for different forms of energy. On our residential/commercial electricity supply bill, the amount of electric energy consumed is measured in kilowatt-hours (KW-h). The energy produced within the object during conduction or convention, which is called Thermal (Heat) Energy, is measured in calories or BTUs (British Thermal units). A calorie is defined as the amount of energy required to raise the temperature of 1 gram of water by 1°C (Celsius). Similarly, a BTU is the amount of energy necessary to upend the temperature of 1 pound of water by 1°F (Fahrenheit). There are also special units for light energy, magnetic energy, sound energy, radiant energy and electric field energy. Considering the fact that all of these special units of energy are still measuring energy, we can convert these from one unit to another. For example, if you want to convert “36 ergs in foot-pounds'', then using the unit converter, you can easily find that 36 ergs equal 2.65522e-6 foot-pounds. (That is 0.00000265522 foot-pounds. Ergs are small.)

1 erg equals 10 joules, 1 BTU is 1055.06 Joules and 1 KW-h is 3.6 million Joules respectively. It is quite simple today to convert from one unit to another. You can easily use Google or Converter for unit conversions. One conversion worth measuring for everyone is for nutritional energy. Certain food items like pizzas contain about 260 “calories” but these are not the same calories that engineers and scientists use. These are Nutritional “calories” that are kilocalories (1000 calories).

We can find the dimension of mass density using the following equation.

The Dimensional Formula of Linear Mass Density = M1L-1T0. The SI unit of Linear Mass Density is kg m-1. Remember that the linear mass density is the quantity of mass per unit length. Here length refers to the basic meter quantity.

FAQ (Frequently Asked Questions)

Q1. What is the Dimension of Density?

Ans: A density is described as the physical property of a matter or substance. The dimension of density is the measurement of how dense the substance is composed of. As per the International System of Units, the unit of density is kg/m^{3}. Note that the density of a given substance changes with the temperature and the pressure. The ideal gas law, for example, reveals the density of the gas is ascertained by the temperature and the pressure of the system.

Q2. What is the Dimension of Relative Density?

Ans: Firstly, relative density has no dimensions, meaning that it is a dimensionless quantity. It is because the density is measurable in units of kg/m^{3}. However, relative density is defined as the density of a substance relative to the density of water. This is generally cited as albeit erroneously. You must be wondering about: how much heavier the substance is than the water? The density of water equals 1000 kg/ m^{3}. Then, while dividing the density of a substance by that of water, we remove the units. Seeing that both contain the same dimensions, thus their ratio is dimensionless.

Q3. When the Water Attains its Maximum Density?

Ans: The Swiss-born British geologist and meteorologist Jean André Deluc discovered that water attains its maximum density at 4° C (39° F). He also brought into view with his theory that the amount of water vapour in any given space is independent of the density of the air in which it is spread out.

Q4. What is the Use of the Dimension of Mass Density?

Ans: Linear densities are primarily applicable to long, thin objects. Note that linear mass density is different from density.