Question

Water rises in a capillary tube of radius $r$ up to a height $h$. The mass of water in the capillary is $m$. The mass of water that will rise in a capillary tube of radius $\frac{r}{3}$ will be

• A. $3m$
• B. $\frac{m}{3}$
• C. $m$
• D. $\frac{2m}{3}$

Hint:

This principle can be memorized as a rule of thumb: for any given liquid, height is inversely proportional to radius ($h \propto 1/r$), but mass is directly proportional to radius ($m \propto r$). If the radius decreases by a factor of 3, the mass must drop by a factor of 3 automatically!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Relate the height and mass of a liquid column to its radius using proportionality principles.

Step 2: Key Formula or Approach:
For a given liquid under capillary action or similar constraints, height scales inversely with radius (h ∝ 1/r), while mass scales directly with radius (m ∝ r).

Step 3: Detailed Explanation:
These two proportionalities form a convenient rule of thumb. If the radius shrinks by a factor of 3, the height triples, but the mass—being directly proportional to radius—drops by exactly that same factor of 3. This inverse-direct pairing allows you to determine how each physical quantity responds to radius changes without re-deriving the full equations each time.

Step 4: Final Answer:
Reducing radius by a factor of 3 decreases mass by a factor of 3.