Question 204: Units , Dimensions and Error Analysis

Question

The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 $$	imes$$ 10-2 m
rise of water, h = 1.45 $$	imes$$ 10-2m
Using g = 9.80 m/s2 and the simplified relation T = $${{rhg} \over 2} 	imes {10^3}N/m$$,  the possible error in surface tension is closest to :

Accepted Answer

Surface tension,
T = $${{rhg} \over 2} 	imes {10^3}N/m$$
Relative error,
$${{\Delta T} \over T} = {{\Delta r} \over r} + {{\Delta h} \over h}$$
Percentage error,
$${{\Delta T} \over T} 	imes 100 = {{\Delta r} \over r} 	imes 100 + {{\Delta h} \over h} 	imes 100$$
$${{\Delta T} \over T} 	imes 100 = \left( {{{{{10}^{ - 2}} 	imes 0.01} \over {1.25 	imes {{10}^{ - 2}}}} + {{{{10}^{ - 2}} 	imes 0.01} \over {1.45 	imes {{10}^{ - 2}}}}} ight) 	imes 100$$
= (0.8 + 0.689) = 1.489 % = 1.5 %

Answer

10 %

Answer

0.15 %

Answer

1.5 %

Answer

2.4 %

Units , Dimensions and Error Analysis

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