Properties of Matter 4 Question 7
9. A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
(2018 Adv.)
(a) For a given material of the capillary tube, $h$ decreases with increase in $r$
(b) For a given material of the capillary tube, $h$ is independent of $\sigma$
(c) If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases
(d) $h$ is proportional to contact angle $\theta$
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Answer:
Correct Answer: 9. (a, c)
Solution:
- $h=\frac{2 \sigma \cos \theta}{r \rho g}$
(a) $\rightarrow h \propto \frac{1}{r}$
(b) $h$ depends upon $\sigma$.
(c) If lift is going up with constant acceleration.
$$ g _{\text {eff }}=(g+a) \Rightarrow h=\frac{2 \sigma \cos \theta}{r \rho(g+a)} $$
It means $h$ decreases.
(d) $h$ is proportional to $\cos \theta$.
