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Rev. Notes > AS > Measuring techniques
 
 
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Topics
 
Measurements Errors Random error
Systematic error Uncertainty Total uncertainity in addition / subtraction
Total uncertainty in multiplication and division Total uncertainty in power factor Total uncertainty in the average value of many measurements
Total uncertainty in the timing experiment Total uncertainty in the timing experiment Example 1 - Calculation of uncertainty
Least count Spring Balance Digital Balance
Protractor Micrometer Vernier calliper
Digital Ammeter Cathode Ray Osciloscope
 

Example 1 - Calculation of uncertainty

Example 1: the diameter and length of a metal cylinder measured with the help of vernier callipers of least count 0.01 cm are 1.22 cm and 5.35 cm. Calculate the volume V of the cylinder and uncertainty in it.
Solution: Given data is
                        Diameter d = 1022 cm with least count 0.01 cm
                                      Length l = 5.35 cm with least count 0.01 cm
Absolute uncertainty in length = 0.01 cm
            %age uncertainty in length = (0.01 cm / 5.53 cm ) X (100 / 100) = 0.2%
Absolute uncertainty in diameter = 0.01 cm
            %age uncertainty in diameter = (0.01 cm / 1.22 cm) X  (100 / 100)= 0.8%
As volume                               V = (πd2l) / 4
Therefore total uncertainty in V = 2 (%age uncertainty in diameter)
                                                            + (%age uncertainty in length)
                                                            =2 × 0.8 + 0.2 = 1.8%
Then V = 3.14 X (0.61 cm)2 X 5.35 cm / 4  = 6.2509079 cm³ with 1.8% uncertainty
Thus                            V = (6.2 ± 0.1) cm³
Where 6.2 cm³ is calculated volume and 0.1 cm³ is the uncertainty in it.

 
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View Comments on this Chapter - Total Comments (2)
 
unknown Said :
^to calculate the radius, diameter needs to be divided by 2. thus, 1.22/2 = 0.61
 
  02/01/15 12:33 AM
   
Bilal Said :
where did 0.6 come from in result
 
  09/09/14 02:51 PM
 

 

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