Fluid Dynamics

Use Stokes’ law:
Convert radius: , , ,

The flow rate through the hole can be determined using Torricelli’s law. After applying the law and calculating, we find the flow rate to be . Thus, the correct answer is option (3).

We apply the continuity equation: Where: - and - - , Substitute the areas and velocities: Cancel : Solve for : Thus, the velocity at the constriction is 5.55 m/s.

Step 1: Relate terminal velocity to radius.
For a small spherical object falling through a viscous medium (like air), the terminal velocity ( ) is given by Stokes' Law (assuming density of fluid is negligible compared to density of object): Where is the radius, is acceleration due to gravity, is the density of the raindrop, is the density of air, and is the viscosity of air. Since , , , and are constants for this scenario: So, for the two raindrops: Step 2: Relate linear momentum to mass and velocity.
Linear momentum ( ) is given by .
The mass ( ) of a spherical raindrop is . Therefore, the momentum of a raindrop is:
For the two raindrops: Step 3: Substitute the velocity ratio into the momentum ratio.
We are given and . Substitute from (1) into (2): Step 4: Solve for the ratio of radii.
To find , take the fifth root of both sides: So, . The final answer is .