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Units and Measurement

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Physics Part I

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Physics

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Class 10 Class 12

The velocity v of a particle at time t is given by straight v equals at plus fraction numerator straight b over denominator straight t plus straight c end fraction comma where a, b and c are constants, The dimensions of a, b and c are respectively:

  • open square brackets LT to the power of negative 2 end exponent close square brackets comma space open square brackets straight L close square brackets space and space open square brackets straight T close square brackets
  • open square brackets straight L squared close square brackets space open square brackets straight T close square brackets space and space open square brackets LT squared close square brackets
  • open square brackets LT squared close square brackets comma space open square brackets LT close square brackets space and space open square brackets straight L close square brackets
  • open square brackets straight L close square brackets comma space open square brackets LT close square brackets space and space open square brackets straight T squared close square brackets

A.

open square brackets LT to the power of negative 2 end exponent close square brackets comma space open square brackets straight L close square brackets space and space open square brackets straight T close square brackets

According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same.
   The given expression is 
                      straight v equals at plus fraction numerator straight b over denominator straight t plus straight c end fraction
From principle of homogeneity
     open square brackets straight a close square brackets space open square brackets straight t close square brackets space equals space open square brackets straight v close square brackets
space space space space space open square brackets straight a close square brackets space equals space fraction numerator open square brackets straight v close square brackets over denominator open square brackets straight t close square brackets end fraction space equals space fraction numerator open square brackets LT to the power of negative 1 end exponent close square brackets over denominator open square brackets straight T close square brackets end fraction space equals space open square brackets LT to the power of negative 2 end exponent close square brackets
Similarly comma space space open square brackets straight c close square brackets space equals space open square brackets straight t close square brackets space equals space open square brackets straight T close square brackets
Further comma space space space space space fraction numerator open square brackets straight b close square brackets over denominator open square brackets straight t plus straight c close square brackets end fraction space equals open square brackets straight v close square brackets

or space space space space space space space space space space space space open square brackets straight b close square brackets space equals space open square brackets straight v close square brackets space open square brackets straight t plus straight c close square brackets
or space space space space space space space space space space space space open square brackets straight b close square brackets space equals space open square brackets LT to the power of negative 1 end exponent close square brackets space open square brackets straight T close square brackets space equals space open square brackets straight L close square brackets

According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same.
   The given expression is 
                      straight v equals at plus fraction numerator straight b over denominator straight t plus straight c end fraction
From principle of homogeneity
     open square brackets straight a close square brackets space open square brackets straight t close square brackets space equals space open square brackets straight v close square brackets
space space space space space open square brackets straight a close square brackets space equals space fraction numerator open square brackets straight v close square brackets over denominator open square brackets straight t close square brackets end fraction space equals space fraction numerator open square brackets LT to the power of negative 1 end exponent close square brackets over denominator open square brackets straight T close square brackets end fraction space equals space open square brackets LT to the power of negative 2 end exponent close square brackets
Similarly comma space space open square brackets straight c close square brackets space equals space open square brackets straight t close square brackets space equals space open square brackets straight T close square brackets
Further comma space space space space space fraction numerator open square brackets straight b close square brackets over denominator open square brackets straight t plus straight c close square brackets end fraction space equals open square brackets straight v close square brackets

or space space space space space space space space space space space space open square brackets straight b close square brackets space equals space open square brackets straight v close square brackets space open square brackets straight t plus straight c close square brackets
or space space space space space space space space space space space space open square brackets straight b close square brackets space equals space open square brackets LT to the power of negative 1 end exponent close square brackets space open square brackets straight T close square brackets space equals space open square brackets straight L close square brackets

502 Views

Define physical quantity.

 


A measurable quantity in terms of which laws of Physics can be expressed is called physical quantity.

The result of a measurement of a physical quantity is expressed by a number accompanied by a unit.


878 Views

What is the need of measurement?

To get the complete knowledge of any physical quantity, measurement is needed. Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. Knowledge without measurement is incomplete and unsatisfactory. 
825 Views

Define unit.

The quantity used as a standard of measurement is called unit. 

Example: Unit of time is second. 

1172 Views

What is measurement?

Measurement is the process of attaching a numeric value to an aspect of a natural phenomenon. Measurement is making the quantitative knowledge of a physical quantity. 
1289 Views

Give four examples of physical quantities.

Examples of Physical quantitie are force, mass, density and power.
821 Views