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Home » Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by force due to the weight of the water. The surface tension of water is . The inner diameter of the capillary tube is nearly A)B)C)D)
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 63 \times 10^{-4} \mathrm{~N} force due to the weight of the water. The surface tension of water is 7 \times 10^{-2} \mathrm{~N} / \mathrm{m}. The inner diameter of the capillary tube is nearly (\pi=22 / 7)
A)6.3 \times 10^{-1} \mathrm{~m}
B)3 \times 10^{-2} \mathrm{~m}
C)7 \times 10^{-2} \mathrm{~m}
D)9 \times 10^{-2} \mathrm{~m}
Physics
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 63 \times 10^{-4} \mathrm{~N} force due to the weight of the water. The surface tension of water is 7 \times 10^{-2} \mathrm{~N} / \mathrm{m}. The inner diameter of the capillary tube is nearly (\pi=22 / 7)
A)6.3 \times 10^{-1} \mathrm{~m}
B)3 \times 10^{-2} \mathrm{~m}
C)7 \times 10^{-2} \mathrm{~m}
D)9 \times 10^{-2} \mathrm{~m}

Correct answer is B.

Upwards force due to surface tension,
F_{u}=(2 \pi R) \times T
where, 2 \pi R \rightarrow circumference of tube
F_{u}=(2 \pi R) \times T
Because surface tension is force per unit length,
\begin{array}{l} \Rightarrow 75 \times 10^{-4}=(2 \pi R) \times 6 \times 10^{-2} \\ (2 R)=\frac{75 \times 10^{-4}}{6 \times 10^{-2}\times \pi}=3 \times 10^{-2} \mathrm{~m} \end{array}

i

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