A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ moof a  particle in terms of its speed v and the speed of light, c. (This relation first arose asa consequence of special relativity due to Albert Einstein). A boy recalls the relationalmost correctly but forgets where to put the constant c. He writes :Guess where to put the missing c. from Physics Units and Measurement Class 11 Manipur Board
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Physics Part I

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Class 10 Class 12
A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ moof a  particle in terms of its speed v and the speed of light, c. (This relation first arose as
a consequence of special relativity due to Albert Einstein). A boy recalls the relation
almost correctly but forgets where to put the constant c. He writes :
straight m space equals space fraction numerator straight m subscript straight o over denominator left parenthesis square root of 1 minus straight v squared end root right parenthesis to the power of bevelled 1 half end exponent end fraction

Guess where to put the missing c.


Given the relation, 

straight m space equals space fraction numerator straight m subscript straight o over denominator left parenthesis square root of 1 minus straight v squared end root right parenthesis to the power of bevelled 1 half end exponent end fraction 

Dimension of m = M1 L0 T0

Dimension of mo = M1 L0 T

Dimension of v = M0 L1 T–1

Dimension of v2 = M0 L2 T–2

Dimension of c = M0 L1 T–1

The given formula will be dimensionally correct only when the dimension of L.H.S is the same as that of R.H.S.

This is possible when the factor in the denominator is dimensionless. This is only possible if straight nu squared space is space divided space by space straight c squared. 
Hence the correct relation is 

straight m space equals space straight m subscript straight o over open parentheses 1 minus begin display style straight v squared over straight c squared end style close parentheses to the power of bevelled 1 half end exponent

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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. 
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Define unit.

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

Example: Unit of time is second. 

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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.


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Give four examples of physical quantities.

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