The following observations were taken for determining surface tension $T$ of water by capillary method:
diameter of capillary, $D = 1.25\times10^{-2}$ m
rise of water, $h = 1.45\times10^{-2}$ m
Using $g = 9.80\ \text{m s}^{-2}$ and the simplified relation $T = \dfrac{rhg}{2}\times10^{3}\ \text{N m}^{-1}$, the possible error in surface tension is closest to:
Answer: (C) $1.5\%$
In $T = \dfrac{rhg}{2}\times10^3$ the quantities multiply, so the fractional errors add. Each reading's error is taken as one unit of its last digit.
- $r = D/2$: $\dfrac{\Delta D}{D} = \dfrac{0.01}{1.25} = 0.8\%$
- $\dfrac{\Delta h}{h} = \dfrac{0.01}{1.45} \approx 0.69\%$
- $\dfrac{\Delta g}{g} = \dfrac{0.01}{9.80} \approx 0.10\%$
$$\frac{\Delta T}{T} \approx 0.8\% + 0.69\% + 0.10\% \approx 1.6\%$$
The closest option is $1.5\%$.
Solution by Sreeraj P, M.Sc Physics