Page 16 - 11-phy-1 Measurements

1. Measurements eLearn.Punjab

As uncertainty is multiplied by power factor, it increases the precision demand of measurement. If
the radius of a small sphere is measured as 2.25 cm by a vernier callipers with least count 0.01 cm,
then the radius r is recorded as

= r 2.25 ± 0.01 cm For Your Information

Absolute uncertainty = Least count = ± 0.01 cm

%age uncertainty in r = 0.01 cm × 100 = 0.4%
2.25 cm

Total percentage uncertainty in V = 3 × 0.4 = 1.2%

Thus volume V = 4 pr3
3

( ) = 4 × 3.14 × 2.25 cm 3
3
= 47.689 cm3 with 1.2% uncertainty

Thus the result should be recorded as
V = 47.7 ± 0.6 cm3

4. For uncertainty in the average value of many
measurements.

(i) Find the average value of measured values.
(ii) Find deviation of each measured value from the

average value.
(iii) The mean deviation is the uncertainty in the average

value.
For example, the six readings of the micrometer screw
gauge to measure the diameter of a wire in mm are

1.20,1.22,1.23,1.19,1.22,1.21.

Then Average = 1.20 + 1.22 + 1.23 + 1.19 + 1.22 + 1.21
6

= 1.21 mm

Some Specific Temperatures

16 v: 1.1