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, $h=1.45\times {10}^{-2}m$.
Using $g=9.80m/s^2$ and the simplified relation. $T=\frac{rhg}{2}\times {10}^{3}N/m$, the possible error in surface tension is closest to :

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

Answer 1

Answer: (C)

$1.5\%$

$T=\frac{rhg}{2}\times {10}^{3}N/m=\frac{Dhg}{4}\times {10}^{3}N/m$ (Since D = 2r)
$\Rightarrow \log T=\log D+\log h+\log g-4+3$
$\Rightarrow \frac{△T}{T}=\frac{△D}{D}+\frac{△h}{h}$
$=\frac{0.01}{1.25}+\frac{0.01}{1.45}=0.015=1.5\%$
Hence correct answer is option (3).