Why does a dimensionless quantity may have a unit?

Dimensionless quantities on the other hand are the quantities which do not possess any dimensions. As these quantities are often a pure ratio between similar physical quantities they do not possess dimension and hence no units.

What does it mean when a unit is dimensionless?

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the unit one (or 1), which is not explicitly shown.

Can dimensionless quantity have a unit?

Yes, A dimensionless quantity may have units. one common example is that of angles whose units are degrees or radians but are dimensionless. also moles is a unit but is dimensionless.

Which is a dimensionless quantity never has unit?

A dimensionless quantity has no dimensions but it may or may not have units. Two very common examples f dimensionless quantities are refractive index which does not have any units and angle which has units (degrees, radians). So, the correct answer would be option(c).

What is the value of a dimensionless quantity in dimensional analysis?

In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all the units cancel out.

Which among the following quantity is a dimensionless quantity?

Answer: 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.

Which one of the following is a dimensionless quantity?

Therefore strain is a dimensionless quantity.

Which one is a quantity with unit but without dimension?

plane angle
(a) A plane angle is an example of a physical quantity which has unit but no dimension since, plane angle = arc/radius in radian & solid angle.

Can a physical quantity have units but still be dimensionless 1?

The answer is Yes, There are such unit quantities, but dimensional quantities. Note: The dimension quantity with one as a quantity that is not associated with any physical dimension. With dimension one, it is a pure number.

Which one is not a dimensional quantity?

This means that angular momentum is not a dimensionless quantity. Therefore, no given quantities are dimensionless. So, the correct answer is “Option D”.