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?

Options

A. For a given material of the capillary Lube, 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`.

Answer

A, C

Explanation

Capillary rise can be written as `h=(2 sigma cos theta)/(pgr)`
We can understand that h decreases whe r increases.
We can see that h depends on `sigma`,
When lift is going up with constant acceleration `h=(2 sigma cos theta)/(p(g+a)r)`.
In the above expression, we can see that effective acceleration due to gravity increases to (g+a), hence h decreases.
We can clearly see that h is proportional to cos `theta`.