Question

Find the percentage change in height risen by liquid if density of fluid, radius of capillary, and surface tension of liquid are decreased by 1%. Assume contact angle doesn’t change and capillary is of sufficient length.

• A. +1%
• B. -1%
• C. +3%
• D. -3%

Hint:

In capillary rise, the height depends on the surface tension, radius, and density, with inversely proportional dependence on density and radius.

Answer 1

The Correct Option is A

Step 1: Formula for height in capillary rise.
The height of the liquid risen in a capillary tube is given by: \[ h = \frac{2 T \cos \theta}{r \rho g}, \] where: - \( T \) is the surface tension of the liquid, - \( \theta \) is the contact angle, - \( r \) is the radius of the capillary, - \( \rho \) is the density of the liquid, and - \( g \) is the acceleration due to gravity. Step 2: Effect of changes.
When the density \( \rho \), radius \( r \), and surface tension \( T \) are decreased by 1%, the height \( h \) will change accordingly. Since \( h \) is inversely proportional to \( \rho \) and \( r \), and directly proportional to \( T \), the height will increase by approximately 1%. Final Answer: \[ \boxed{+1\%}. \]