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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 the error in the measurement of radius of sphere is 2%, then the error in the determination of volume of the sphere will be

  • 4%

  • 6%

  • 8%

  • 2%


B.

6%

Volume space of space straight a space sphere space equals space 4 over 3 straight pi space left parenthesis radius right parenthesis cubed
or space straight V space equals space 4 over 3 πR cubed
Taking space logarithium space on space both space sides comma space we space have space
log space straight V space equals space log space 4 over 3 space πR cubed
Taking space logarithium space on space both space sides comma space we space have
log space straight V space equals space log space 4 over 3 straight pi space plus 3 space log space straight R
Differentiating comma space we space get comma
fraction numerator increment straight V over denominator straight V end fraction space equals space 0 space plus fraction numerator 3 increment straight R over denominator straight R end fraction
Accordingly comma space fraction numerator increment straight R over denominator straight R end fraction space equals 2 percent sign
Thus comma space fraction numerator increment straight V over denominator straight V end fraction space equals space 3 space straight x space 2 percent sign space equals space 6 percent sign 
Volume space of space straight a space sphere space equals space 4 over 3 straight pi space left parenthesis radius right parenthesis cubed
or space straight V space equals space 4 over 3 πR cubed
Taking space logarithium space on space both space sides comma space we space have space
log space straight V space equals space log space 4 over 3 space πR cubed
Taking space logarithium space on space both space sides comma space we space have
log space straight V space equals space log space 4 over 3 straight pi space plus 3 space log space straight R
Differentiating comma space we space get comma
fraction numerator increment straight V over denominator straight V end fraction space equals space 0 space plus fraction numerator 3 increment straight R over denominator straight R end fraction
Accordingly comma space fraction numerator increment straight R over denominator straight R end fraction space equals 2 percent sign
Thus comma space fraction numerator increment straight V over denominator straight V end fraction space equals space 3 space straight x space 2 percent sign space equals space 6 percent sign 
456 Views

Define unit.

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

Example: Unit of time is second. 

1172 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 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 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