Question:
Two soap bubbles have radii in the ratio of 2:1. What is the ratio of excess pressures inside them?
Two soap bubbles have radii in the ratio of 2:1. What is the ratio of excess pressures inside them?
Updated On: Jul 28, 2022
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The Correct Option is A
Solution and Explanation
Excess pressure inside the bubble, $ p=\frac{4T}{r} $ Then, $ {{p}_{1}}=\frac{4T}{{{r}_{1}}} $ ... (i) $ {{p}_{2}}=\frac{4T}{{{r}_{2}}} $ ...(ii) From Eqs. (i) and (ii), we have $ \frac{{{p}_{1}}}{{{p}_{2}}}=\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{{{r}_{2}}}{{{r}_{1}}} $ $ \frac{{{p}_{1}}}{{{p}_{2}}}=\frac{1}{2} $
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.