The following observations were taken for dtermining the surface tension of water by capillary tube method: diameter of capillary , `D = 1.25 xx 10^(-2) m` and rise of water in capillary , `h = 1.45 xx 10^(-2) m`. Taking ` g = 9.80 m s^(-2)` and using the relation `T = ( r gh//2) xx 10^(3) N m^(-1)`, what is the possible error in measurement of surface tension `T`?
(a) `2.4%` (b) `15%` (c) `1.6%` (d) 0.15%`

Options

A. 0.024
B. 0.1
C. 0.0015
D. 0.015

Answer

(d)

Explanation

Given surface tension, `T = (r h g)/(2)xx10^3`
`(DeltaT)/(T) = (Delta r)/(r ) + (Delta h)/(h) + 0`
% error in surface tension
`(DeltaT)/(T)xx100 =((Delta r)/(r ) + (Delta h)/(h))xx100 = ((DeltaD)/(D) + (Delta h)/(h))xx100`
`=((0.01)/(1.25) + (0.01)/(1.45))xx100 = (0.8 + 0.689)xx100`
`= 1.489% ~~ 1.5%`