Properties of Matter 4 Question 1
3. The following observations were taken for determining surface tension $T$ of water by capillary method. Diameter of capillary, $d=1.25 \times 10^{-2} \mathrm{~m}$ rise of water, $h=1.45 \times 10^{-2} \mathrm{~m}$. Using $g=9.80 \mathrm{~m} / \mathrm{s}^2$ and the simplified relation $T=\frac{r h g}{2} \times 10^3 \mathbf{N} / \mathbf{m}$, the possible error in surface tension is closest to
(2017 Main)
(a) $1.5 \%$
(b) $2.4 \%$
(c) $10 \%$
(d) $0.15 \%$
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Answer:
Correct Answer: 3. (a)
Solution:
- By ascent formula, we have surface tension,
$$ \begin{aligned} T & =\frac{r h g}{2} \times 10^{3} \frac{N}{m} \\ & =\frac{d h g}{4} \times 10^{3} \frac{N}{m} \end{aligned} $$
$$ \begin{aligned} & \Rightarrow \quad \frac{\Delta T}{T}=\frac{\Delta d}{d}+\frac{\Delta h}{h} \quad \text { [given, } g \text { is constant] } \\ & \text { So, percentage }=\frac{\Delta T}{T} \times 100=\left(\frac{\Delta d}{d}+\frac{\Delta h}{h}\right) \times 100 \end{aligned} $$
$$ \begin{aligned} & =\left(\frac{0.01 \times 10^{-2}}{1.25 \times 10^{-2}}+\frac{0.01 \times 10^{-2}}{1.45 \times 10^{-2}}\right) \times 100 \\ & =1.5 \% \\ \therefore \quad \frac{\Delta T}{T} \times 100 & =1.5 \% \end{aligned} $$
