Question

Give examples for the following:

a) A dimensionless and unitless physical quantity.
b) A dimensionless physical quantity but having unit in SI system.
c) Two physical quantities which have the same dimensions.

Answer 1

Answer:

a) refractive index. Hint: We know from dimensional analysis, a physical quantity which has no dimension is called a dimensionless quantity. It is also known as a scalar quantity. This is often seen when taking the ratio between two identical dimensions or similar dimensions.

b) Dimensionless quantity is also known as the quantity of dimension with one as a quantity which is not related to any physical dimension. It is a pure number with dimension 1.

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Example Of Dimensionless Quantity With Unit.

Physical quantityUnitSolid angleSteradiansAtomic massAMU = 1.66054 x 10-27kg

c) Work and Torque are the two physical quantity having the same dimension [ML²T-²].

Explanation:

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Answer 2

It is a pure number with dimension 1. These dimensionless quantities are widely used in Maths and Physics.
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