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. `1.5 % `
B. `2.4 % `
C. `10 % `
D. `0.15 % `

Answer

A

Explanation

`T=(rhg)/(2)xx10^(3)N//m=(dhg)/(4)xx10^(3)N//m" "%"error"(DeltaT)/(T)=(Deltad)/(d)+(Deltah)/(h)`
`Rightarrow(DeltaT)/(T)xx100=((0.01xx10^(-2))/(1.25xx10^(-2))+(0.01xx10^(-2))/(1.45xx10^(-2)))xx100=0.8%+0.7%=1.5%`
(There is no error in g because its value is not calculated through experiments)