A drop oil is spread on a oil of volume 10-10m3 spreads out on water to make circular film of ratios 10-1m. What is the thickness of the film
volume = area * thickness
now just plug in your numbers
To find the thickness of the film, we need to use the given information about the volume and the area ratio.
Given:
Volume of the oil drop: 10^(-10) m³
Area ratio of the film: 10:1
First, let's calculate the area of the circular film:
Area of the circular film = π * radius²
The area ratio gives us the relationship between the areas of the drop and the film:
Area of the drop / Area of the film = 10:1
Let's assume the radius of the drop is r₁ and the radius of the film is r₂. Since the area of the drop is equal to the volume of the drop (in this case), we have:
π * (r₁)² / (π * (r₂)²) = 10/1
Simplifying:
(r₁)² / (r₂)² = 10/1
Taking the square root of both sides:
r₁ / r₂ = √(10/1)
Next, let's find the volume of the circular film:
Volume of the film = π * (r₂)² * thickness
Since the volume of the oil drop has spread out to form the circular film, the volume of the drop must equal the volume of the film:
Volume of the drop = Volume of the film
10^(-10) m³ = π * (r₂)² * thickness
Now, we can solve for the thickness of the film by rearranging the equation:
thickness = 10^(-10) m³ / (π * (r₂)²)
To find the value of r₂, we can substitute the relationship between r₁ and r₂ that we found earlier:
r₁ / r₂ = √(10/1)
Simplifying:
r₂ = r₁ / √(10/1)
Now we can substitute this value of r₂ into the previous equation to find the thickness of the film:
thickness = 10^(-10) m³ / (π * (r₁ / √(10/1))²)
Simplifying:
thickness = 10^(-10) / (π * (r₁² / (10/1)))
thickness = (10^(-10) * (1/10)) / (π * r₁²)
Finally, we have the expression to calculate the thickness of the film. To obtain the actual value, we need to know the radius of the oil drop (r₁).