In a liquid there is air bubble of radius 1 mm at a depth 10 cm below the free space. The surf

Name: Problem 47, Chapter 12: Arihant AIEEE Physics
Uploaded: 2021-09-11T12:13:25-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: In a liquid there is air bubble of radius 1 mm at a depth 10 cm below the free space. The surface tension of liquid is 0.075 N / m and density is 1000 kg / m^3. By what amount is the pressure inside the bubble greater than the atmospheric pressure? (a) 1130 pascal (b) 1200 pascal (c) 1100 pascal (d) 1000 pascal

step 1 In this problem, the radius of the bubble is given as r is equal to 1 m m. Changing it in meter,

Question

In a liquid there is air bubble of radius $1 \mathrm{~mm}$ at a depth $10 \mathrm{~cm}$ below the free space. The surface tension of liquid is $0.075 \mathrm{~N} / \mathrm{m}$ and density is $1000 \mathrm{~kg} / \mathrm{m}^{3}$. By what amount is the pressure inside the bubble greater than the atmospheric pressure? (a) 1130 pascal (b) 1200 pascal (c) 1100 pascal (d) 1000 pascal

   In a liquid there is air bubble of radius $1 \mathrm{~mm}$ at a depth $10 \mathrm{~cm}$ below the free space. The surface tension of liquid is $0.075 \mathrm{~N} / \mathrm{m}$ and density is $1000 \mathrm{~kg} / \mathrm{m}^{3}$. By what amount is the pressure inside the bubble greater than the atmospheric pressure?
(a) 1130 pascal
(b) 1200 pascal
(c) 1100 pascal
(d) 1000 pascal

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 12, Problem 47

Instant Answer

Solved by Expert Narayan Hari

09/11/2021

Step 1

We know that 1 mm = 0.001 m. So, the radius R of the bubble is 0.001 m. Show more…

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In a liquid there is air bubble of radius $1 \mathrm{~mm}$ at a depth $10 \mathrm{~cm}$ below the free space. The surface tension of liquid is $0.075 \mathrm{~N} / \mathrm{m}$ and density is $1000 \mathrm{~kg} / \mathrm{m}^{3}$. By what amount is the pressure inside the bubble greater than the atmospheric pressure? (a) 1130 pascal (b) 1200 pascal (c) 1100 pascal (d) 1000 pascal

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Key Concepts

Laplace Pressure

Laplace pressure is the extra pressure inside a curved surface, such as a bubble, due to surface tension. For a spherical bubble, it is given by the formula ?P = (2?)/R, where ? is the surface tension and R is the radius, accounting for the additional pressure required to balance the forces acting across the curved interface.

Surface Tension

Surface tension is the property of a liquid's surface that causes it to behave like a stretched elastic membrane. It creates an inward force at the interface between a liquid and another phase, affecting the shape and stability of bubbles and droplets.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid due to the force of gravity acting on the fluid's mass. It increases with depth according to the relation ?P = ?gh, where ? is the density, g is the acceleration due to gravity, and h is the depth below the fluid's free surface.

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