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

Answer

D

Explanation

`"Surface tension, T"=(rhg)/(2)xx10^(3)`
Relative error in surface tension, `(DeltaT)/(T)=(Deltar)/(r)+(Deltah)/(h)+0`
`" "(because g, 2 and 10^(3)" are constant")`
`"Percentage error"`
`100xx(DeltaT)/(T)=((10^(-2)xx0.01)/(1.25xx10^(-2))+(10^(-2)xx0.01)/(1.45xx10^(-2)))100`
`=(0.8+0.689)=(1.489)=1.489%~=1.5%`