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Excess pressure can be (2T//R) for...

Excess pressure can be `(2T//R)` for

A

spherical drop

B

spherical meniscus

C

cylindrical bubble in air

D

spherical bubble in water

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The correct Answer is:
To determine the conditions under which excess pressure can be expressed as \( \frac{2T}{R} \), we will analyze various scenarios involving drops and bubbles. ### Step-by-Step Solution: 1. **Understanding Excess Pressure**: Excess pressure is defined as the difference in pressure between the inside and outside of a liquid drop or bubble. It is influenced by the surface tension of the liquid and the radius of curvature of the surface. 2. **Spherical Liquid Drop**: For a spherical liquid drop, the formula for excess pressure is given by: \[ \Delta P = \frac{2T}{R} \] where \( T \) is the surface tension and \( R \) is the radius of the drop. This is because a spherical drop has only one free surface. 3. **Spherical Meniscus**: Similar to a spherical drop, a spherical meniscus (like that formed in a liquid in a curved container) also has the same excess pressure: \[ \Delta P = \frac{2T}{R} \] Again, this is due to the presence of a single free surface. 4. **Cylindrical Bubble in Air**: For a cylindrical bubble, there are two free surfaces (the inside and outside surfaces of the bubble). The excess pressure is given by: \[ \Delta P = \frac{T}{R} \] However, if we consider the total effect of both surfaces, the excess pressure becomes: \[ \Delta P = \frac{2T}{R} \] This is because each surface contributes to the overall pressure difference. 5. **Spherical Bubble in Water**: For a spherical bubble submerged in water, the excess pressure is given by: \[ \Delta P = \frac{T}{R} \] This is because the bubble has only one free surface exposed to the water. ### Conclusion: The excess pressure can be expressed as \( \frac{2T}{R} \) for: - A spherical liquid drop - A spherical meniscus - A cylindrical bubble in air

To determine the conditions under which excess pressure can be expressed as \( \frac{2T}{R} \), we will analyze various scenarios involving drops and bubbles. ### Step-by-Step Solution: 1. **Understanding Excess Pressure**: Excess pressure is defined as the difference in pressure between the inside and outside of a liquid drop or bubble. It is influenced by the surface tension of the liquid and the radius of curvature of the surface. 2. **Spherical Liquid Drop**: ...
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