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

143027 The work done in blowing a soap bubble of surface tension $0.06 \mathrm{Nm}^{-1}$ from $2 \mathrm{~cm}$ radius to 5 cm radius is

1 $0.004168 \mathrm{~J}$
2 $0.003168 \mathrm{~J}$
3 $0.003158 \mathrm{~J}$
4 $0.004568 \mathrm{~J}$
Mechanical Properties of Fluids

143029 When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}\right.$ $>r_{1}$ ) coalesce, the radius of curvature of common surface is

1 $r_{2}-r_{1}$
2 $\frac{r_{2}-r_{1}}{r_{1} r_{2}}$
3 $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
4 $\mathrm{r}_{2}+\mathrm{r}_{1}$
Mechanical Properties of Fluids

143030 The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is (T-surface tension of the solution)

1 $4 \pi\left(D^{2}-d^{2}\right) T$
2 $8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}$
3 $\pi\left(D^{2}-d^{2}\right) T$
4 $2 \pi\left(D^{2}-d^{2}\right) T$
Mechanical Properties of Fluids

143031 Consider an air bubble of radius $2 \mathrm{~mm}$ in a liquid at a depth of $5 \mathrm{~cm}$ below the free surface. The density of the liquid is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the surface tension is $0.1 \mathrm{~N} / \mathrm{m}$. Then, find the pressure inside the air bubble is greater than the pressure at the free surface of the liquid. (Take, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $500 \mathrm{~Pa}$
2 $600 \mathrm{~Pa}$
3 $700 \mathrm{~Pa}$
4 $800 \mathrm{~Pa}$
Mechanical Properties of Fluids

143032 Consider a water droplet of diameter $0.2 \mathrm{~mm}$ where the outside pressure is $1.5 \mathrm{~N} / \mathrm{cm}^{2}$ at $25^{\circ} \mathrm{C}$. the pressure inside the droplet, when the surface tension at $25^{\circ} \mathrm{C}$ is $0.08 \mathrm{~N} / \mathrm{m}$ is

1 $0.32 \mathrm{~N} / \mathrm{cm}^{2}$
2 $1.18 \mathrm{~N} / \mathrm{cm}^{2}$
3 $1.82 \mathrm{~N} / \mathrm{cm}^{2}$
4 $1.66 \mathrm{~N} / \mathrm{cm}^{2}$
Mechanical Properties of Fluids

143027 The work done in blowing a soap bubble of surface tension $0.06 \mathrm{Nm}^{-1}$ from $2 \mathrm{~cm}$ radius to 5 cm radius is

1 $0.004168 \mathrm{~J}$
2 $0.003168 \mathrm{~J}$
3 $0.003158 \mathrm{~J}$
4 $0.004568 \mathrm{~J}$
Mechanical Properties of Fluids

143029 When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}\right.$ $>r_{1}$ ) coalesce, the radius of curvature of common surface is

1 $r_{2}-r_{1}$
2 $\frac{r_{2}-r_{1}}{r_{1} r_{2}}$
3 $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
4 $\mathrm{r}_{2}+\mathrm{r}_{1}$
Mechanical Properties of Fluids

143030 The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is (T-surface tension of the solution)

1 $4 \pi\left(D^{2}-d^{2}\right) T$
2 $8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}$
3 $\pi\left(D^{2}-d^{2}\right) T$
4 $2 \pi\left(D^{2}-d^{2}\right) T$
Mechanical Properties of Fluids

143031 Consider an air bubble of radius $2 \mathrm{~mm}$ in a liquid at a depth of $5 \mathrm{~cm}$ below the free surface. The density of the liquid is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the surface tension is $0.1 \mathrm{~N} / \mathrm{m}$. Then, find the pressure inside the air bubble is greater than the pressure at the free surface of the liquid. (Take, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $500 \mathrm{~Pa}$
2 $600 \mathrm{~Pa}$
3 $700 \mathrm{~Pa}$
4 $800 \mathrm{~Pa}$
Mechanical Properties of Fluids

143032 Consider a water droplet of diameter $0.2 \mathrm{~mm}$ where the outside pressure is $1.5 \mathrm{~N} / \mathrm{cm}^{2}$ at $25^{\circ} \mathrm{C}$. the pressure inside the droplet, when the surface tension at $25^{\circ} \mathrm{C}$ is $0.08 \mathrm{~N} / \mathrm{m}$ is

1 $0.32 \mathrm{~N} / \mathrm{cm}^{2}$
2 $1.18 \mathrm{~N} / \mathrm{cm}^{2}$
3 $1.82 \mathrm{~N} / \mathrm{cm}^{2}$
4 $1.66 \mathrm{~N} / \mathrm{cm}^{2}$
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Mechanical Properties of Fluids

143027 The work done in blowing a soap bubble of surface tension $0.06 \mathrm{Nm}^{-1}$ from $2 \mathrm{~cm}$ radius to 5 cm radius is

1 $0.004168 \mathrm{~J}$
2 $0.003168 \mathrm{~J}$
3 $0.003158 \mathrm{~J}$
4 $0.004568 \mathrm{~J}$
Mechanical Properties of Fluids

143029 When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}\right.$ $>r_{1}$ ) coalesce, the radius of curvature of common surface is

1 $r_{2}-r_{1}$
2 $\frac{r_{2}-r_{1}}{r_{1} r_{2}}$
3 $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
4 $\mathrm{r}_{2}+\mathrm{r}_{1}$
Mechanical Properties of Fluids

143030 The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is (T-surface tension of the solution)

1 $4 \pi\left(D^{2}-d^{2}\right) T$
2 $8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}$
3 $\pi\left(D^{2}-d^{2}\right) T$
4 $2 \pi\left(D^{2}-d^{2}\right) T$
Mechanical Properties of Fluids

143031 Consider an air bubble of radius $2 \mathrm{~mm}$ in a liquid at a depth of $5 \mathrm{~cm}$ below the free surface. The density of the liquid is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the surface tension is $0.1 \mathrm{~N} / \mathrm{m}$. Then, find the pressure inside the air bubble is greater than the pressure at the free surface of the liquid. (Take, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $500 \mathrm{~Pa}$
2 $600 \mathrm{~Pa}$
3 $700 \mathrm{~Pa}$
4 $800 \mathrm{~Pa}$
Mechanical Properties of Fluids

143032 Consider a water droplet of diameter $0.2 \mathrm{~mm}$ where the outside pressure is $1.5 \mathrm{~N} / \mathrm{cm}^{2}$ at $25^{\circ} \mathrm{C}$. the pressure inside the droplet, when the surface tension at $25^{\circ} \mathrm{C}$ is $0.08 \mathrm{~N} / \mathrm{m}$ is

1 $0.32 \mathrm{~N} / \mathrm{cm}^{2}$
2 $1.18 \mathrm{~N} / \mathrm{cm}^{2}$
3 $1.82 \mathrm{~N} / \mathrm{cm}^{2}$
4 $1.66 \mathrm{~N} / \mathrm{cm}^{2}$
Mechanical Properties of Fluids

143027 The work done in blowing a soap bubble of surface tension $0.06 \mathrm{Nm}^{-1}$ from $2 \mathrm{~cm}$ radius to 5 cm radius is

1 $0.004168 \mathrm{~J}$
2 $0.003168 \mathrm{~J}$
3 $0.003158 \mathrm{~J}$
4 $0.004568 \mathrm{~J}$
Mechanical Properties of Fluids

143029 When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}\right.$ $>r_{1}$ ) coalesce, the radius of curvature of common surface is

1 $r_{2}-r_{1}$
2 $\frac{r_{2}-r_{1}}{r_{1} r_{2}}$
3 $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
4 $\mathrm{r}_{2}+\mathrm{r}_{1}$
Mechanical Properties of Fluids

143030 The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is (T-surface tension of the solution)

1 $4 \pi\left(D^{2}-d^{2}\right) T$
2 $8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}$
3 $\pi\left(D^{2}-d^{2}\right) T$
4 $2 \pi\left(D^{2}-d^{2}\right) T$
Mechanical Properties of Fluids

143031 Consider an air bubble of radius $2 \mathrm{~mm}$ in a liquid at a depth of $5 \mathrm{~cm}$ below the free surface. The density of the liquid is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the surface tension is $0.1 \mathrm{~N} / \mathrm{m}$. Then, find the pressure inside the air bubble is greater than the pressure at the free surface of the liquid. (Take, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $500 \mathrm{~Pa}$
2 $600 \mathrm{~Pa}$
3 $700 \mathrm{~Pa}$
4 $800 \mathrm{~Pa}$
Mechanical Properties of Fluids

143032 Consider a water droplet of diameter $0.2 \mathrm{~mm}$ where the outside pressure is $1.5 \mathrm{~N} / \mathrm{cm}^{2}$ at $25^{\circ} \mathrm{C}$. the pressure inside the droplet, when the surface tension at $25^{\circ} \mathrm{C}$ is $0.08 \mathrm{~N} / \mathrm{m}$ is

1 $0.32 \mathrm{~N} / \mathrm{cm}^{2}$
2 $1.18 \mathrm{~N} / \mathrm{cm}^{2}$
3 $1.82 \mathrm{~N} / \mathrm{cm}^{2}$
4 $1.66 \mathrm{~N} / \mathrm{cm}^{2}$
Mechanical Properties of Fluids

143027 The work done in blowing a soap bubble of surface tension $0.06 \mathrm{Nm}^{-1}$ from $2 \mathrm{~cm}$ radius to 5 cm radius is

1 $0.004168 \mathrm{~J}$
2 $0.003168 \mathrm{~J}$
3 $0.003158 \mathrm{~J}$
4 $0.004568 \mathrm{~J}$
Mechanical Properties of Fluids

143029 When two soap bubbles of radius $r_{1}$ and $r_{2}\left(r_{2}\right.$ $>r_{1}$ ) coalesce, the radius of curvature of common surface is

1 $r_{2}-r_{1}$
2 $\frac{r_{2}-r_{1}}{r_{1} r_{2}}$
3 $\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
4 $\mathrm{r}_{2}+\mathrm{r}_{1}$
Mechanical Properties of Fluids

143030 The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is (T-surface tension of the solution)

1 $4 \pi\left(D^{2}-d^{2}\right) T$
2 $8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}$
3 $\pi\left(D^{2}-d^{2}\right) T$
4 $2 \pi\left(D^{2}-d^{2}\right) T$
Mechanical Properties of Fluids

143031 Consider an air bubble of radius $2 \mathrm{~mm}$ in a liquid at a depth of $5 \mathrm{~cm}$ below the free surface. The density of the liquid is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the surface tension is $0.1 \mathrm{~N} / \mathrm{m}$. Then, find the pressure inside the air bubble is greater than the pressure at the free surface of the liquid. (Take, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $500 \mathrm{~Pa}$
2 $600 \mathrm{~Pa}$
3 $700 \mathrm{~Pa}$
4 $800 \mathrm{~Pa}$
Mechanical Properties of Fluids

143032 Consider a water droplet of diameter $0.2 \mathrm{~mm}$ where the outside pressure is $1.5 \mathrm{~N} / \mathrm{cm}^{2}$ at $25^{\circ} \mathrm{C}$. the pressure inside the droplet, when the surface tension at $25^{\circ} \mathrm{C}$ is $0.08 \mathrm{~N} / \mathrm{m}$ is

1 $0.32 \mathrm{~N} / \mathrm{cm}^{2}$
2 $1.18 \mathrm{~N} / \mathrm{cm}^{2}$
3 $1.82 \mathrm{~N} / \mathrm{cm}^{2}$
4 $1.66 \mathrm{~N} / \mathrm{cm}^{2}$