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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

If energy (E), velocity (v) and time (T) are chosen  as the fundamental quantities, the dimensional formula of surface tension will be

  • [Ev-2T-1]

  • [Ev-1T-2]

  • [Ev-2T-2]

  • [E-2v-1T-3]


C.

[Ev-2T-2]

We space know space that
surface space tension space left parenthesis straight S right parenthesis space equals space fraction numerator Force space left square bracket straight F right square bracket over denominator Length space left square bracket straight L right square bracket end fraction
so comma space left square bracket straight S right square bracket space equals space fraction numerator MLT to the power of negative 2 end exponent over denominator left square bracket straight L right square bracket end fraction space equals space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket
Energy space left parenthesis straight E right parenthesis space equals space force space straight x space displacement
rightwards double arrow space left square bracket straight E right square bracket space equals space left square bracket ML squared straight T squared right square bracket
velocity space left parenthesis straight v right parenthesis space equals displacement over time
left square bracket straight v right square bracket space equals space left square bracket LT to the power of negative 1 end exponent right square bracket

straight S proportional to space straight E to the power of straight a straight v to the power of straight b straight T to the power of straight c
Where space straight a comma space straight b comma space straight c space are space constants
From space the space principle space of space homogeneity
left square bracket LHS right square bracket space equals left square bracket RHS right square bracket
rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket ML squared straight T to the power of negative 2 end exponent right square bracket to the power of straight a space left square bracket LT to the power of negative 1 end exponent right square bracket to the power of straight b left square bracket straight T right square bracket to the power of straight c
rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket straight M to the power of straight a straight L to the power of 2 straight a plus straight b end exponent space straight T to the power of negative 2 straight a minus straight b plus straight c end exponent right square bracket
Equating space the space power space on space both space sides comma space we space get
straight a equals space 1 comma space 2 straight a space plus straight b space equals 0 comma space straight b equals negative 2
minus 2 straight a minus straight b plus straight c space equals negative 2

straight c equals space left parenthesis 2 straight a plus straight b right parenthesis minus 2 space equals space 0 minus 2 space equals negative 2
left square bracket straight S right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket
We space know space that
surface space tension space left parenthesis straight S right parenthesis space equals space fraction numerator Force space left square bracket straight F right square bracket over denominator Length space left square bracket straight L right square bracket end fraction
so comma space left square bracket straight S right square bracket space equals space fraction numerator MLT to the power of negative 2 end exponent over denominator left square bracket straight L right square bracket end fraction space equals space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket
Energy space left parenthesis straight E right parenthesis space equals space force space straight x space displacement
rightwards double arrow space left square bracket straight E right square bracket space equals space left square bracket ML squared straight T squared right square bracket
velocity space left parenthesis straight v right parenthesis space equals displacement over time
left square bracket straight v right square bracket space equals space left square bracket LT to the power of negative 1 end exponent right square bracket

straight S proportional to space straight E to the power of straight a straight v to the power of straight b straight T to the power of straight c
Where space straight a comma space straight b comma space straight c space are space constants
From space the space principle space of space homogeneity
left square bracket LHS right square bracket space equals left square bracket RHS right square bracket
rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket ML squared straight T to the power of negative 2 end exponent right square bracket to the power of straight a space left square bracket LT to the power of negative 1 end exponent right square bracket to the power of straight b left square bracket straight T right square bracket to the power of straight c
rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket straight M to the power of straight a straight L to the power of 2 straight a plus straight b end exponent space straight T to the power of negative 2 straight a minus straight b plus straight c end exponent right square bracket
Equating space the space power space on space both space sides comma space we space get
straight a equals space 1 comma space 2 straight a space plus straight b space equals 0 comma space straight b equals negative 2
minus 2 straight a minus straight b plus straight c space equals negative 2

straight c equals space left parenthesis 2 straight a plus straight b right parenthesis minus 2 space equals space 0 minus 2 space equals negative 2
left square bracket straight S right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket
6867 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

Give four examples of physical quantities.

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

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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