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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
A physical quantity P is related to four observables a, b, c and d as follows : 
straight P space equals space straight a cubed straight b squared space divided by space square root of straight c straight d
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value ofP calculated using the above relation turns out to be 3.763, to what value should you round off the result? 

Given space comma space

straight P space equals space fraction numerator straight a cubed straight b squared over denominator open parentheses square root of straight c space straight d close parentheses end fraction space

Maximum space fractional space error space in space straight p space is space given space by comma space

fraction numerator increment straight P over denominator straight P end fraction space equals plus-or-minus open square brackets 3 fraction numerator increment straight a over denominator straight a end fraction space plus 2 fraction numerator increment straight b over denominator straight b end fraction space plus 1 half fraction numerator increment straight c over denominator straight c end fraction plus fraction numerator increment straight d over denominator straight d end fraction close square brackets space

space space space space space space space space space space equals space plus-or-minus space open square brackets 3 1 over 100 space plus 2 3 over 100 space plus 1 half 4 over 100 plus 2 over 100 close square brackets

space space space space space space space space space space equals space plus-or-minus space 13 over 100 space equals space plus-or-minus 0.13 space

That space is comma space

Percentage space error space in space straight P space equals space fraction numerator increment straight P over denominator straight P end fraction cross times 100

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals plus-or-minus 0.13 space cross times space 100 space equals plus-or-minus 13 space percent sign

Value space of space straight P space equals space 3.763

On space rounding space off space the space given space value space to space the space first space place comma space

straight P space equals space 3.8 space
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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 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

Define unit.

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

Example: Unit of time is second. 

1172 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.


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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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