03. Excess of Pressure (Bubbles and Drops)
Mechanical Properties of Fluids

143087 A boy formed a bubble and a liquid drop from the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{~N} / \mathrm{m}^{2}$. If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

1 0
2 $50 \mathrm{~N} / \mathrm{m}^{2}$
3 $100 \mathrm{~N} / \mathrm{m}^{2}$
4 $200 \mathrm{~N} / \mathrm{m}^{2}$
5 $400 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143088 A spherical drop of radius $r$ is divided in to 8 equal droplets. If the surface tension is $S$. then the work done in the process will be

1 $2 \pi r^{2} S$
2 $3 \pi r^{2} \mathrm{~S}$
3 $4 \pi r^{2} S$
4 $4 \pi r^{2} S^{2}$
Mechanical Properties of Fluids

143089 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

1 $\frac{3}{2}$
2 $\frac{2}{3}$
3 $-\frac{2}{3}$
4 8
Mechanical Properties of Fluids

143090 An air bubble of radius $1 \mathrm{~mm}$ is at a depth of 8 $\mathrm{cm}$ below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and $2000\mathrm{~kg} / \mathrm{m}^{3}$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $1500 \mathrm{~N} / \mathrm{m}^{2}$
2 $1800 \mathrm{~N} / \mathrm{m}^{2}$
3 $1600 \mathrm{~N} / \mathrm{m}^{2}$
4 $1700 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143091 A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

1 $12 \pi R^{2} T$
2 $4 \pi R^{2} T$
3 $16 \pi R^{2} T$
4 $24 \pi \mathrm{R}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143087 A boy formed a bubble and a liquid drop from the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{~N} / \mathrm{m}^{2}$. If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

1 0
2 $50 \mathrm{~N} / \mathrm{m}^{2}$
3 $100 \mathrm{~N} / \mathrm{m}^{2}$
4 $200 \mathrm{~N} / \mathrm{m}^{2}$
5 $400 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143088 A spherical drop of radius $r$ is divided in to 8 equal droplets. If the surface tension is $S$. then the work done in the process will be

1 $2 \pi r^{2} S$
2 $3 \pi r^{2} \mathrm{~S}$
3 $4 \pi r^{2} S$
4 $4 \pi r^{2} S^{2}$
Mechanical Properties of Fluids

143089 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

1 $\frac{3}{2}$
2 $\frac{2}{3}$
3 $-\frac{2}{3}$
4 8
Mechanical Properties of Fluids

143090 An air bubble of radius $1 \mathrm{~mm}$ is at a depth of 8 $\mathrm{cm}$ below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and $2000\mathrm{~kg} / \mathrm{m}^{3}$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $1500 \mathrm{~N} / \mathrm{m}^{2}$
2 $1800 \mathrm{~N} / \mathrm{m}^{2}$
3 $1600 \mathrm{~N} / \mathrm{m}^{2}$
4 $1700 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143091 A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

1 $12 \pi R^{2} T$
2 $4 \pi R^{2} T$
3 $16 \pi R^{2} T$
4 $24 \pi \mathrm{R}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143087 A boy formed a bubble and a liquid drop from the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{~N} / \mathrm{m}^{2}$. If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

1 0
2 $50 \mathrm{~N} / \mathrm{m}^{2}$
3 $100 \mathrm{~N} / \mathrm{m}^{2}$
4 $200 \mathrm{~N} / \mathrm{m}^{2}$
5 $400 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143088 A spherical drop of radius $r$ is divided in to 8 equal droplets. If the surface tension is $S$. then the work done in the process will be

1 $2 \pi r^{2} S$
2 $3 \pi r^{2} \mathrm{~S}$
3 $4 \pi r^{2} S$
4 $4 \pi r^{2} S^{2}$
Mechanical Properties of Fluids

143089 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

1 $\frac{3}{2}$
2 $\frac{2}{3}$
3 $-\frac{2}{3}$
4 8
Mechanical Properties of Fluids

143090 An air bubble of radius $1 \mathrm{~mm}$ is at a depth of 8 $\mathrm{cm}$ below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and $2000\mathrm{~kg} / \mathrm{m}^{3}$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $1500 \mathrm{~N} / \mathrm{m}^{2}$
2 $1800 \mathrm{~N} / \mathrm{m}^{2}$
3 $1600 \mathrm{~N} / \mathrm{m}^{2}$
4 $1700 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143091 A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

1 $12 \pi R^{2} T$
2 $4 \pi R^{2} T$
3 $16 \pi R^{2} T$
4 $24 \pi \mathrm{R}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143087 A boy formed a bubble and a liquid drop from the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{~N} / \mathrm{m}^{2}$. If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

1 0
2 $50 \mathrm{~N} / \mathrm{m}^{2}$
3 $100 \mathrm{~N} / \mathrm{m}^{2}$
4 $200 \mathrm{~N} / \mathrm{m}^{2}$
5 $400 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143088 A spherical drop of radius $r$ is divided in to 8 equal droplets. If the surface tension is $S$. then the work done in the process will be

1 $2 \pi r^{2} S$
2 $3 \pi r^{2} \mathrm{~S}$
3 $4 \pi r^{2} S$
4 $4 \pi r^{2} S^{2}$
Mechanical Properties of Fluids

143089 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

1 $\frac{3}{2}$
2 $\frac{2}{3}$
3 $-\frac{2}{3}$
4 8
Mechanical Properties of Fluids

143090 An air bubble of radius $1 \mathrm{~mm}$ is at a depth of 8 $\mathrm{cm}$ below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and $2000\mathrm{~kg} / \mathrm{m}^{3}$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $1500 \mathrm{~N} / \mathrm{m}^{2}$
2 $1800 \mathrm{~N} / \mathrm{m}^{2}$
3 $1600 \mathrm{~N} / \mathrm{m}^{2}$
4 $1700 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143091 A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

1 $12 \pi R^{2} T$
2 $4 \pi R^{2} T$
3 $16 \pi R^{2} T$
4 $24 \pi \mathrm{R}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143087 A boy formed a bubble and a liquid drop from the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{~N} / \mathrm{m}^{2}$. If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

1 0
2 $50 \mathrm{~N} / \mathrm{m}^{2}$
3 $100 \mathrm{~N} / \mathrm{m}^{2}$
4 $200 \mathrm{~N} / \mathrm{m}^{2}$
5 $400 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143088 A spherical drop of radius $r$ is divided in to 8 equal droplets. If the surface tension is $S$. then the work done in the process will be

1 $2 \pi r^{2} S$
2 $3 \pi r^{2} \mathrm{~S}$
3 $4 \pi r^{2} S$
4 $4 \pi r^{2} S^{2}$
Mechanical Properties of Fluids

143089 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

1 $\frac{3}{2}$
2 $\frac{2}{3}$
3 $-\frac{2}{3}$
4 8
Mechanical Properties of Fluids

143090 An air bubble of radius $1 \mathrm{~mm}$ is at a depth of 8 $\mathrm{cm}$ below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and $2000\mathrm{~kg} / \mathrm{m}^{3}$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $1500 \mathrm{~N} / \mathrm{m}^{2}$
2 $1800 \mathrm{~N} / \mathrm{m}^{2}$
3 $1600 \mathrm{~N} / \mathrm{m}^{2}$
4 $1700 \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143091 A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

1 $12 \pi R^{2} T$
2 $4 \pi R^{2} T$
3 $16 \pi R^{2} T$
4 $24 \pi \mathrm{R}^{2} \mathrm{~T}$