Properties Of Fluids

Step 1: Understanding the Concept:
When drops coalesce, the total volume remains constant but the total surface area decreases. This reduction in surface area leads to the release of surface energy ( ).
Step 2: Detailed Explanation:
Let be the radius of the big drop.
Volume conservation: .
Initial surface area .
Final surface area .
Decrease in area .
Energy released .
Step 3: Final Answer:
The energy released is .

Concept: Surface energy: where is surface tension and is surface area. When a liquid drop breaks into smaller drops, surface area increases, hence surface energy increases.
Step 1:Find radius of original drop} Diameter mm
Step 2:Relation of radii} Volume conserved:
Step 3:Surface areas} Initial surface area: Final surface area:
Step 4:Increase in surface area}
Step 5:Increase in surface energy} Thus Closest option:

Step 1: Understanding the Concept:
Terminal velocity depends on the square of the radius of the sphere. When a large drop breaks into smaller droplets, the total volume remains constant, allowing us to find the relationship between the old and new radii.
Step 2: Key Formula or Approach:
1. Terminal velocity .
2. Volume conservation: , where is the number of droplets.
Step 3: Detailed Explanation:
1. Find new radius : . 2. Find ratio of velocities: Since and : Substituting :
Step 4: Final Answer:
The ratio is 16.

Step 1: Understanding the Question:
We need to calculate the terminal velocity of a metallic sphere falling through a viscous liquid (glycerine). Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is moving equals the force of gravity.
Step 2: Key Formula or Approach:
The formula for terminal velocity ( ) is given by Stokes' law, which comes from balancing the gravitational force, buoyant force, and viscous drag force:
where:
- = radius of the sphere
- = acceleration due to gravity
- = density of the sphere
- = density of the fluid
- = viscosity of the fluid
Step 3: Detailed Explanation:
First, we must ensure all units are consistent. The options are in cm/s, so using the CGS (Centimeter-Gram-Second) system is convenient.
- Diameter = 2 mm, so radius .
- Density of sphere .
- Density of glycerine .
- Viscosity of glycerine . (Note: 1 poise = 1 g·cm ·s , which is the CGS unit).
- Acceleration due to gravity .
Now substitute these values into the terminal velocity formula:
Step 4: Final Answer:
The terminal velocity attained by the sphere is 2.0 cm/s.