Viscosity

Concept: Physics (Mechanical Properties of Fluids) – Capillary Action and Jurin's Law.

Step 1: Relate height to radius. According to Jurin's Law, the height to which a liquid rises in a capillary is inversely proportional to the radius ( ).

Step 2: State the formula for the mass of the liquid column. The mass of the water in the capillary is the product of volume and density ( ). Thus, the relationship is .

Step 3: Combine the relationships. Since , we substitute this into the mass proportionality: .

Step 4: Calculate the new mass for radius . Let be the new mass: . $ $

Step 1: Terminal velocity and radius.
The terminal velocity of a spherical object falling through a fluid is given by: where is the radius of the object. This relation comes from the balance between the gravitational force and the drag force acting on the object.
Step 2: Using the given ratio of radii.
Let the radii of the two rain drops be and , where . The ratio of their terminal velocities will be:
Step 3: Conclusion.
Thus, the ratio of their terminal velocities is , which corresponds to option (C).