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The Question & Answer (Q&A) Knowledge Managenet

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Table of Contents

- Which of the following is a dimensionless number?
- What is meant by dimensionless number?
- Are constants dimensionless?
- What are constants in the universe?
- Are all constants dimensionless or Unitless Why?
- Is refractive index a dimensionless quantity?
- What is the dimensional formula of refractive index?
- What is the unit of refractive index?
- Which of the following is dimensionless quantity refractive index?
- Is Pi a dimensional constant?
- Which physical quantity is Unitless?
- Is a Unitless a quantity?
- Which gradient is Unitless quantity?
- Is specific gravity Unitless quantity?
- What instrument is used to measure specific gravity?
- What is the proper formula for calculating specific gravity?
- Why specific gravity is important?
- What does a specific gravity of 1.025 mean?

All pure numbers are dimensionless quantities, for example 1, i, π, e, and φ. Units of number such as the dozen, gross, googol, and Avogadro’s number may also be considered dimensionless.

A number representing a property of a physical system, but not measured on a scale of physical units (as of time, mass, or distance). Drag coefficients and stress, for example, are measured as dimensionless numbers.

example, universal gravitational constant, Planck’s constant etc. do have dimensions.

They include the velocity of light in vacuum (c); the charge of the electron, the absolute value of which is the fundamental unit of electric charge (e); the mass of the electron (me); Planck’s constant (h); and the fine-structure constant, symbolized by the Greek letter alpha.

Answer. All constants are unit less and we know the system or constant which ar2 unit less are always going to be dimensionless because we derive the dimension of a system from its unit only …..

n is the refractive index of the medium. v is the velocity of light in that particular medium. c is the velocity of the light in vacuum. So, we can say that the refractive index is a dimensionless quantity.

Refractive Index is defined as the relative speed at which light moves through a material with respect to its speed in vacuum. As both the values belong to same quantity (speed), units get nullified. So Refractive Index is dimensionless quantity. Dimensional Formula of Refractive Index = M^0L^0T^0.

Unit of refractive index (μ) will be the ratio of the unit of speed of light in vacuum(c) to the speed of light in the given medium(v). As you can see, the unit of refractive is 1, which means the refractive index is just a number without any unit.

The reason is that, Refractive Index is generally expressed as ratio of two velocities of light under different mediums. Hence, in dimensional form, they appear only as Velocity / Velocity. So both cancel out each other and give us a dimensionless quantity. Hence Refractive Index is the correct answer.

As a first step, we list the variables and dimensional constants (if any) assumed to be relevant. (a). as required and expected. The reader can also easily verify that both π1 and π2 in (e) are indeed dimensionless, i.e., their dimensions are 1.

Certain quantities are defined as the ratio of two quantities of the same kind, and are thus dimensionless. A dimensionless physical quantity may have an unit (e.g. Mechanical equivalent of heat) but a unitless physical quantity is always dimensionless (e.g. Coefficient of friction , refractive index).

A unit less quantity is the one in which there are no fundamental quantities involved. It doesn’t have any unit and hence it doesn’t have any dimensions. The dimension is Zero. Examples are, angle, elastic strain, Poisson’s ratio etc.

quantities displacement gradient

Explanation: Specific gravity is a dimensionless quantity; that is, it is not expressed in units. Materials with a specific gravity less than 1 are less dense than water, and will float on the pure liquid; substances with a specific gravity more than 1 are more dense than water, and will sink.

Hydrometers

The formula for specific gravity, given that the reference substance is water, is the density of the object divided by the density of the water.

Significance and Use 4.1 Specific gravity is an important property of fluids being related to density and viscosity. Knowing the specific gravity will allow determination of a fluid’s characteristics compared to a standard, usually water, at a specified temperature.

Specific gravity is usually 1.010-1.025 (normal range: 1.003-1.030) and highest in the morning. A value >1.025 indicates normal concentrating ability. A value >1.035-1.040 suggests possible contamination, very high levels of glucose, or recently received low-molecular-weight dextran or high-density radiopaque dyes.