Question 409: Properties of Matter

Question

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 $$	heta .$$ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Accepted Answer

We know that,
$$h = {{2\sigma \cos 	heta } \over {r\,ho g}}$$..... (1)
where r is inner radius of capillary tube; $$\sigma$$ is surface tension; $$	heta$$ is angle between water and wall of capillary tube; h is height of water in capillary tube and g is acceleration due to gravity. From Eq. (1),
$$h \propto {1 \over r}$$
Therefore, for a given material of the capillary tube, h decreases with increase in r.
Hence, option (A) is correct.
h depends on $$\sigma$$, therefore option (B) is incorrect.
In a lift going up with a constant acceleration a, the force due to surface tension remains same but weight of the water increases i.e., W
lift
= $$\pi$$r
2
h$$ho$$(g + a). Thus, the height of the water rise in a capillary becomes
$$h = {{2\sigma \cos 	heta } \over {r\,ho (g + a)}} = {{2\sigma \cos 	heta } \over {r\, ho{g_{eff}}}}$$,
where g
eff
is the effective g in the lift. Hence, h decrease if the experiment is performed in a lift going up with a constant acceleration.
From (1), h $$\propto$$ cos$$	heta$$ and not $$	heta$$, therefore, option (D) is incorrect.

Answer

For a given material of the capillary tube, $$h$$ decreases with increase in $$r$$

Answer

For a given material of the capillary tube, $$h$$ is independent of $$\sigma $$

Answer

If this experiment is performed in a lift going up with a constant acceleration, then $$h$$ decreases

Answer

$$h$$ is proportional to contact angle $$	heta $$

Properties of Matter

Choose the correct answer: