Question

Water rises in a capillary tube of radius \( r \) upto a height \( h \). The mass of water in a capillary is \( m \). The mass of water that will rise in a capillary of radius \( \frac{r}{4} \) will be

• A. \( \frac{m}{4} \)
• B. \( m \)
• C. \( 4m \)
• D. \( m \)

Hint:

The capillary rise is proportional to \( \frac{1}{r} \) and the mass of water is proportional to \( r^2 \).

Answer 1

The Correct Option is A

Step 1: Understanding capillary rise.
The height to which water rises in a capillary tube is inversely proportional to the radius of the tube. That is, the capillary rise for a tube with radius \( r/4 \) is four times greater than that for a tube with radius \( r \).
Step 2: Conclusion.
The mass of water that rises is proportional to the cross-sectional area of the tube, which depends on the square of the radius. Therefore, the mass of water in the tube with radius \( r/4 \) will be \( \frac{m}{4} \).