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

Answer

C

Explanation

Here the information of least count of D and h measurement are not given, so we will use max. permissible error in D and h= place value of last digit
`D=1.25xx10^(-2)m` so `DeltaD = 0.01xx10^(-2)m`
`h=1.45xx10^(-2)` m so `Deltah=0.01xx10^(-2)m`
` g=9.80m//s^2`
` T = (rgh)/2 xx10^3`
`(DeltaT)/T = (Deltar)/r +(Deltah)/h=(DeltaD)/D+(Deltah)/h`
`(DeltaT)/T=(0.01 xx10^(-2))/(1.25xx10^(-2))+(0.01 xx10^(-2))/(1.45 xx10^(-2))`
`(DeltaT)/T xx100% = (1/(125)+1/145)xx100%`
`= (0.008 +0.0069)xx100% =1.49 ~~1.5%`.