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%, then 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 capillarity, mass of liquid raised is directly proportional to tube radius.

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 ∝ r
Step 3: If r increases by 50%: m' = 1.5m = (3)/(2)m