Question

Water rises in a capillary tube of radius r upto height h . The mass of water in a capillary is m. The mass of water that will rise in capillary of radius $\frac{r}{5}$ will be}

• A. $\frac{m}{5}$
• B. $\frac{m}{2}$
• C. m
• D. $\frac{m}{25}$

Hint:

Height $\propto 1/r$, but Mass $\propto r$.

Answer 1

The Correct Option is A

Step 1: Relations
Capillary rise $h \propto \frac{1}{r}$.
Mass of liquid in capillary $m = \rho V = \rho (\pi r^2 h)$.
Step 2: Substitution
Since $h = \frac{k}{r}$, then $m = \rho \pi r^2 (\frac{k}{r}) = \rho \pi k r$.
This implies $m \propto r$.
Step 3: Calculation
New mass $m' \propto r/5 \implies m' = \frac{m}{5}$.
Final Answer: (A)