Question

A capillary tube of radius r is immersed vertically in a liquid such that liquid rises in it to height h (less than the length of the tube). Mass of liquid in the capillary tube is m. If radius of the capillary tube is increased by 50%, the mass of liquid that will rise in the tube is:

• A. \(\dfrac{2}{3}m\)
• B. \(m\)
• C. \(\dfrac{3}{2}m\)
• D. (9)/(4)m

Hint:

In capillary rise problems: m ∝ r because height decreases but volume increases faster.

Answer 1

The Correct Option is C

Step 1: Height of capillary rise: h=(2Tcosθ)/(ρ g r)
Step 2: Mass of liquid: m=ρ π r² h
Step 3: Substituting h: m ∝ r
Step 4: If radius increases by 50%: r' = 1.5r ⟹ m' = 1.5m = (3)/(2)m