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Mechanical Properties Of Fluids

Question
CBSEENPH11020340

The following observations were taken for determining surface tension T of water by the capillary method :
Diameter of capillary, D = 1.25 × 10–2 m rise of water, h = 1.45 × 10–2 m
Using g = 9.80 m/s2 and the simplified relation T = (rhg/2) x103 n/m, the possible error in surface tension is closest to:

  • 2.4%

  • 10%

  • 0.15%

  • 1.5%

Solution

D.

1.5%

straight T space equals space rhg over 2 space straight x space 10 cubed
fraction numerator increment straight T over denominator straight T end fraction space equals space fraction numerator increment straight r over denominator straight r end fraction space plus space fraction numerator increment straight h over denominator straight h end fraction space plus 0
100 space straight x space fraction numerator increment straight T over denominator straight T end fraction space equals space open parentheses fraction numerator 10 to the power of negative 2 end exponent space straight x space.01 over denominator 1.25 space straight x space 10 to the power of negative 2 end exponent end fraction space plus fraction numerator 10 to the power of negative 2 end exponent space straight x space 0.1 over denominator 1.45 space straight x space 10 to the power of negative 2 end exponent end fraction close parentheses 100
space equals space 0.8 space plus 0.689
equals space 1.489
space 100 space straight x space fraction numerator increment straight T over denominator straight T end fraction space equals space 1.489 percent sign
space approximately equal to space 1.5 space percent sign