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 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.

 Yunzila Said : but we have calculated the value with the given radius then what is the need of division by 2......??? 07/12/17 12:21 PM

 Yunzila Said : why in the ans is 0.6.......??? bcz after calculation we get 1.2.....!!! 07/12/17 12:17 PM

 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