01. Surface Tension and Surface Energy
Mechanical Properties of Fluids

142776 Surface tension of a soap bubble is $2.0 \times 10^{-2}$ $\mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be : Take $\left[\pi=\frac{22}{7}\right]$

1 $9.24 \times 10^{-4} \mathrm{~J}$
2 $18.48 \times 10^{-4} \mathrm{~J}$
3 $0.72 \times 10^{-4} \mathrm{~J}$
4 $5.76 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142777 If $\mathbf{1 0 0 0}$ droplets of water of surface tension 0.07 $\mathrm{N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to form a single drop. In the process the released surface energy is : $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

1 $8.8 \times 10^{-5} \mathrm{~J}$
2 $7.92 \times 10^{-4} \mathrm{~J}$
3 $7.92 \times 10^{-6} \mathrm{~J}$
4 $9.68 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142778 A soap bubble of radius $r$ is blown upto form a bubble of radius $2 \mathrm{r}$ under isothermal conditions. If $\pi \sigma$ is the surface tension of soap solution, the energy spent in doing so is

1 $6 \pi \sigma r^{2}$
2 $3 \pi \sigma r^{2}$
3 $24 \pi \sigma r^{2}$
4 $12 \pi \sigma r^{2}$
5 $9 \pi \sigma r^{2}$
Mechanical Properties of Fluids

142779 A ring cut with an inner radius $4.85 \mathrm{~cm}$ and outer radius $4.95 \mathrm{~cm}$ is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is $70 \times 10^{-3} \mathrm{Nm}^{-1}$, then the extra mass in the other pan required to pull the ring away from water is

1 $2 \mathrm{~g}$
2 $3 \mathrm{~g}$
3 $4.4 \mathrm{~g}$
4 $15 \mathrm{~g}$
5 $10 \mathrm{~g}$
Mechanical Properties of Fluids

142780 Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $\mathbf{R}$ to $3 R$ at given temperature will be

1 $64 \pi \mathrm{SR}^{2}$
2 $\frac{18 \pi \mathrm{SR}^{2}}{3}$
3 $8 \pi \mathrm{SR}^{2}$
4 $16 \pi \mathrm{SR}^{2}$
Mechanical Properties of Fluids

142776 Surface tension of a soap bubble is $2.0 \times 10^{-2}$ $\mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be : Take $\left[\pi=\frac{22}{7}\right]$

1 $9.24 \times 10^{-4} \mathrm{~J}$
2 $18.48 \times 10^{-4} \mathrm{~J}$
3 $0.72 \times 10^{-4} \mathrm{~J}$
4 $5.76 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142777 If $\mathbf{1 0 0 0}$ droplets of water of surface tension 0.07 $\mathrm{N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to form a single drop. In the process the released surface energy is : $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

1 $8.8 \times 10^{-5} \mathrm{~J}$
2 $7.92 \times 10^{-4} \mathrm{~J}$
3 $7.92 \times 10^{-6} \mathrm{~J}$
4 $9.68 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142778 A soap bubble of radius $r$ is blown upto form a bubble of radius $2 \mathrm{r}$ under isothermal conditions. If $\pi \sigma$ is the surface tension of soap solution, the energy spent in doing so is

1 $6 \pi \sigma r^{2}$
2 $3 \pi \sigma r^{2}$
3 $24 \pi \sigma r^{2}$
4 $12 \pi \sigma r^{2}$
5 $9 \pi \sigma r^{2}$
Mechanical Properties of Fluids

142779 A ring cut with an inner radius $4.85 \mathrm{~cm}$ and outer radius $4.95 \mathrm{~cm}$ is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is $70 \times 10^{-3} \mathrm{Nm}^{-1}$, then the extra mass in the other pan required to pull the ring away from water is

1 $2 \mathrm{~g}$
2 $3 \mathrm{~g}$
3 $4.4 \mathrm{~g}$
4 $15 \mathrm{~g}$
5 $10 \mathrm{~g}$
Mechanical Properties of Fluids

142780 Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $\mathbf{R}$ to $3 R$ at given temperature will be

1 $64 \pi \mathrm{SR}^{2}$
2 $\frac{18 \pi \mathrm{SR}^{2}}{3}$
3 $8 \pi \mathrm{SR}^{2}$
4 $16 \pi \mathrm{SR}^{2}$
Mechanical Properties of Fluids

142776 Surface tension of a soap bubble is $2.0 \times 10^{-2}$ $\mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be : Take $\left[\pi=\frac{22}{7}\right]$

1 $9.24 \times 10^{-4} \mathrm{~J}$
2 $18.48 \times 10^{-4} \mathrm{~J}$
3 $0.72 \times 10^{-4} \mathrm{~J}$
4 $5.76 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142777 If $\mathbf{1 0 0 0}$ droplets of water of surface tension 0.07 $\mathrm{N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to form a single drop. In the process the released surface energy is : $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

1 $8.8 \times 10^{-5} \mathrm{~J}$
2 $7.92 \times 10^{-4} \mathrm{~J}$
3 $7.92 \times 10^{-6} \mathrm{~J}$
4 $9.68 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142778 A soap bubble of radius $r$ is blown upto form a bubble of radius $2 \mathrm{r}$ under isothermal conditions. If $\pi \sigma$ is the surface tension of soap solution, the energy spent in doing so is

1 $6 \pi \sigma r^{2}$
2 $3 \pi \sigma r^{2}$
3 $24 \pi \sigma r^{2}$
4 $12 \pi \sigma r^{2}$
5 $9 \pi \sigma r^{2}$
Mechanical Properties of Fluids

142779 A ring cut with an inner radius $4.85 \mathrm{~cm}$ and outer radius $4.95 \mathrm{~cm}$ is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is $70 \times 10^{-3} \mathrm{Nm}^{-1}$, then the extra mass in the other pan required to pull the ring away from water is

1 $2 \mathrm{~g}$
2 $3 \mathrm{~g}$
3 $4.4 \mathrm{~g}$
4 $15 \mathrm{~g}$
5 $10 \mathrm{~g}$
Mechanical Properties of Fluids

142780 Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $\mathbf{R}$ to $3 R$ at given temperature will be

1 $64 \pi \mathrm{SR}^{2}$
2 $\frac{18 \pi \mathrm{SR}^{2}}{3}$
3 $8 \pi \mathrm{SR}^{2}$
4 $16 \pi \mathrm{SR}^{2}$
Mechanical Properties of Fluids

142776 Surface tension of a soap bubble is $2.0 \times 10^{-2}$ $\mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be : Take $\left[\pi=\frac{22}{7}\right]$

1 $9.24 \times 10^{-4} \mathrm{~J}$
2 $18.48 \times 10^{-4} \mathrm{~J}$
3 $0.72 \times 10^{-4} \mathrm{~J}$
4 $5.76 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142777 If $\mathbf{1 0 0 0}$ droplets of water of surface tension 0.07 $\mathrm{N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to form a single drop. In the process the released surface energy is : $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

1 $8.8 \times 10^{-5} \mathrm{~J}$
2 $7.92 \times 10^{-4} \mathrm{~J}$
3 $7.92 \times 10^{-6} \mathrm{~J}$
4 $9.68 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142778 A soap bubble of radius $r$ is blown upto form a bubble of radius $2 \mathrm{r}$ under isothermal conditions. If $\pi \sigma$ is the surface tension of soap solution, the energy spent in doing so is

1 $6 \pi \sigma r^{2}$
2 $3 \pi \sigma r^{2}$
3 $24 \pi \sigma r^{2}$
4 $12 \pi \sigma r^{2}$
5 $9 \pi \sigma r^{2}$
Mechanical Properties of Fluids

142779 A ring cut with an inner radius $4.85 \mathrm{~cm}$ and outer radius $4.95 \mathrm{~cm}$ is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is $70 \times 10^{-3} \mathrm{Nm}^{-1}$, then the extra mass in the other pan required to pull the ring away from water is

1 $2 \mathrm{~g}$
2 $3 \mathrm{~g}$
3 $4.4 \mathrm{~g}$
4 $15 \mathrm{~g}$
5 $10 \mathrm{~g}$
Mechanical Properties of Fluids

142780 Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $\mathbf{R}$ to $3 R$ at given temperature will be

1 $64 \pi \mathrm{SR}^{2}$
2 $\frac{18 \pi \mathrm{SR}^{2}}{3}$
3 $8 \pi \mathrm{SR}^{2}$
4 $16 \pi \mathrm{SR}^{2}$
Mechanical Properties of Fluids

142776 Surface tension of a soap bubble is $2.0 \times 10^{-2}$ $\mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble from $3.5 \mathrm{~cm}$ to $7 \mathrm{~cm}$ will be : Take $\left[\pi=\frac{22}{7}\right]$

1 $9.24 \times 10^{-4} \mathrm{~J}$
2 $18.48 \times 10^{-4} \mathrm{~J}$
3 $0.72 \times 10^{-4} \mathrm{~J}$
4 $5.76 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142777 If $\mathbf{1 0 0 0}$ droplets of water of surface tension 0.07 $\mathrm{N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to form a single drop. In the process the released surface energy is : $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

1 $8.8 \times 10^{-5} \mathrm{~J}$
2 $7.92 \times 10^{-4} \mathrm{~J}$
3 $7.92 \times 10^{-6} \mathrm{~J}$
4 $9.68 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

142778 A soap bubble of radius $r$ is blown upto form a bubble of radius $2 \mathrm{r}$ under isothermal conditions. If $\pi \sigma$ is the surface tension of soap solution, the energy spent in doing so is

1 $6 \pi \sigma r^{2}$
2 $3 \pi \sigma r^{2}$
3 $24 \pi \sigma r^{2}$
4 $12 \pi \sigma r^{2}$
5 $9 \pi \sigma r^{2}$
Mechanical Properties of Fluids

142779 A ring cut with an inner radius $4.85 \mathrm{~cm}$ and outer radius $4.95 \mathrm{~cm}$ is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is $70 \times 10^{-3} \mathrm{Nm}^{-1}$, then the extra mass in the other pan required to pull the ring away from water is

1 $2 \mathrm{~g}$
2 $3 \mathrm{~g}$
3 $4.4 \mathrm{~g}$
4 $15 \mathrm{~g}$
5 $10 \mathrm{~g}$
Mechanical Properties of Fluids

142780 Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $\mathbf{R}$ to $3 R$ at given temperature will be

1 $64 \pi \mathrm{SR}^{2}$
2 $\frac{18 \pi \mathrm{SR}^{2}}{3}$
3 $8 \pi \mathrm{SR}^{2}$
4 $16 \pi \mathrm{SR}^{2}$