Question

Two capillary tubes A and B of diameter 1 mm and 2 mm respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is

• A. 2 cm
• B. 3 cm
• C. 4 cm
• D. 6 cm
• E. 9 cm

Hint:

Capillary rise is inversely proportional to tube radius or diameter.

Answer 1

The Correct Option is B

Understanding the Concept: Capillary rise is given by: \[ h = \frac{2T \cos \theta}{\rho g r} \] Since all quantities except radius are constant: \[ h \propto \frac{1}{r} \propto \frac{1}{d} \]

Step 1: Establish proportionality. \[ \frac{h_1}{h_2} = \frac{d_2}{d_1} \]

Step 2: Substitute given values. \[ \frac{6}{h_2} = \frac{2}{1} \]

Step 3: Solve for \(h_2\). \[ h_2 = \frac{6}{2} = 3 \, \text{cm} \]

Step 4: Final Answer. \[ \boxed{3 \, \text{cm}} \]