Question

The height of the capillary rise of water in the soil is
(A) Inversely proportional to the radius of the tube
(B) Inversely proportional to the density of water
(C) Directly proportional to the radius of the tube
(D) Inversely proportional to the surface tension of water
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (A) only
• C. (A) and (B) only
• D. (D) only

Hint:

Capillary height $\uparrow$ when radius $\downarrow$ and density $\downarrow$.

Answer 1

The Correct Option is C

Step 1: Balance the upward surface-tension force with the weight of the water column to get \( h = \dfrac{2\gamma \cos\theta}{r \rho g} \).
Step 2: From this, \( h \) decreases as radius \( r \) increases, so (A) is true, and \( h \) decreases as density \( \rho \) increases, so (B) is true.
Step 3: \( h \) increases with surface tension \( \gamma \), direct not inverse, so (D) is false, and (C) contradicts (A), so it is false too.
Step 4: Correct option, \[ \boxed{\text{(A) and (B) only}} \]