Question

The following observations were taken for determining the surface tension $T$ of water by capillary rise method. Diameter of the capillary is $D=1.25\times {10}^{2}m$, rise of water in capillary tube is $h=1.45\times {10}^{2}m$, $g=9.80m{s}^{-2}$. Using the relation $T=\left(\frac{rhg}{2}\right)\times {10}^{3}N/m,$ the possible percentage error in surface tension $T$ is:

• A. $0.15\%$
• B. $1.5\%$
• C. $15\%$
• D. $2.4\%$

Answer 1

The correct option is B $1.5\%$

$T=\frac{rhg}{2}\times {10}^3$

$=\frac{Dhg}{4}\times {10}^3$

$⟹\frac{\Delta T}{T}=\frac{\Delta d}{d}+\frac{\Delta h}{h}+\frac{\Delta g}{g}$

$=\frac{0.01\times {10}^2}{1.25\times {10}^2}+\frac{0.01\times {10}^2}{1.45\times {10}^2}+\frac{0.01}{9.80}$

$\approx 0.015$

$⟹$ Percentage error $=\frac{\Delta T}{T}\times 100$% $=1.5$%