Question

The following observations were taken for determining surface tension $T$ of water by capillary method. Diameter of capillary, $D=1.25\times {10}^{-2}m$ rise of water, $h=1.45\times {10}^{-2}\mathrm{m.}$
Using $g=9.80m/s^2$and the simplified relation $T=\frac{rgh}{2}\times {10}^{3}N/m$ , the possible error in surface tension is closest to

• A. 10 %
• B. 0.15 %
• C. 1.5 %
• D. 2.4 %

Answer 1

The correct option is C 1.5 %

$T=\frac{rgh}{2}\times {10}^{3}N/m$
$\Delta r=0.01m\Delta h=0.01m\frac{\Delta T}{T}=\left(\frac{\Delta r}{r}\right|+\left(\frac{\Delta h}{h}\right|=\frac{0.01}{1.25}+\frac{0.01}{1.\mathrm{45\$}}$

$\frac{\Delta T}{T}\times 100=\left(\frac{1}{125}+\frac{1}{145}\right)\times 100=0.8+0.69=1.5\%$