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

143092 Work done in increasing the size of a soap bubble from a radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ is nearly (surface tension of soap solution $=0.05 \mathrm{Nm}^{-1}$ )

1 $(0.70 \pi) \mathrm{mJ}$
2 $(0.64 \pi) \mathrm{mJ}$
3 $(0.30 \pi) \mathrm{mJ}$
4 $(0.58 \pi) \mathrm{mJ}$
Mechanical Properties of Fluids

143094 A water drop of radius $1 \mathrm{~cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be:
[Given $\pi=3.14$ ]

1 $8.5 \times 10^{-4} \mathrm{~J}$
2 $8.2 \times 10^{-4} \mathrm{~J}$
3 $7.5 \times 10^{-4} \mathrm{~J}$
4 $5.3 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

143095 A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 \times 10^{-4} \mathrm{Ncm}^{-1}$. The radius of drop in cm will be: (Take: $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $\frac{15}{\sqrt{2 \rho-\sigma}}$
2 $\frac{15}{\sqrt{\rho-\sigma}}$
3 $\frac{3}{2 \sqrt{\rho-\sigma}}$
4 $\frac{3}{20 \sqrt{2 \rho-\sigma}}$
Mechanical Properties of Fluids

143096 Two glasses with identical volumes are filled with water to the half - way mark and are kept side by side, two solid cubes made of the same metal are now dropped into the two glasses and both of them sink in the water. The first is glasses completely filled now. The second glass is still $\frac{7}{16}^{\text {th }}$ empty. The ratio of the surface areas of the cubes dropped into the first and the second glass is

1 $16: 7$
2 $8: 1$
3 $2: 1$
4 $4: 1$
Mechanical Properties of Fluids

143092 Work done in increasing the size of a soap bubble from a radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ is nearly (surface tension of soap solution $=0.05 \mathrm{Nm}^{-1}$ )

1 $(0.70 \pi) \mathrm{mJ}$
2 $(0.64 \pi) \mathrm{mJ}$
3 $(0.30 \pi) \mathrm{mJ}$
4 $(0.58 \pi) \mathrm{mJ}$
Mechanical Properties of Fluids

143094 A water drop of radius $1 \mathrm{~cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be:
[Given $\pi=3.14$ ]

1 $8.5 \times 10^{-4} \mathrm{~J}$
2 $8.2 \times 10^{-4} \mathrm{~J}$
3 $7.5 \times 10^{-4} \mathrm{~J}$
4 $5.3 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

143095 A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 \times 10^{-4} \mathrm{Ncm}^{-1}$. The radius of drop in cm will be: (Take: $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $\frac{15}{\sqrt{2 \rho-\sigma}}$
2 $\frac{15}{\sqrt{\rho-\sigma}}$
3 $\frac{3}{2 \sqrt{\rho-\sigma}}$
4 $\frac{3}{20 \sqrt{2 \rho-\sigma}}$
Mechanical Properties of Fluids

143096 Two glasses with identical volumes are filled with water to the half - way mark and are kept side by side, two solid cubes made of the same metal are now dropped into the two glasses and both of them sink in the water. The first is glasses completely filled now. The second glass is still $\frac{7}{16}^{\text {th }}$ empty. The ratio of the surface areas of the cubes dropped into the first and the second glass is

1 $16: 7$
2 $8: 1$
3 $2: 1$
4 $4: 1$
Mechanical Properties of Fluids

143092 Work done in increasing the size of a soap bubble from a radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ is nearly (surface tension of soap solution $=0.05 \mathrm{Nm}^{-1}$ )

1 $(0.70 \pi) \mathrm{mJ}$
2 $(0.64 \pi) \mathrm{mJ}$
3 $(0.30 \pi) \mathrm{mJ}$
4 $(0.58 \pi) \mathrm{mJ}$
Mechanical Properties of Fluids

143094 A water drop of radius $1 \mathrm{~cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be:
[Given $\pi=3.14$ ]

1 $8.5 \times 10^{-4} \mathrm{~J}$
2 $8.2 \times 10^{-4} \mathrm{~J}$
3 $7.5 \times 10^{-4} \mathrm{~J}$
4 $5.3 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

143095 A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 \times 10^{-4} \mathrm{Ncm}^{-1}$. The radius of drop in cm will be: (Take: $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $\frac{15}{\sqrt{2 \rho-\sigma}}$
2 $\frac{15}{\sqrt{\rho-\sigma}}$
3 $\frac{3}{2 \sqrt{\rho-\sigma}}$
4 $\frac{3}{20 \sqrt{2 \rho-\sigma}}$
Mechanical Properties of Fluids

143096 Two glasses with identical volumes are filled with water to the half - way mark and are kept side by side, two solid cubes made of the same metal are now dropped into the two glasses and both of them sink in the water. The first is glasses completely filled now. The second glass is still $\frac{7}{16}^{\text {th }}$ empty. The ratio of the surface areas of the cubes dropped into the first and the second glass is

1 $16: 7$
2 $8: 1$
3 $2: 1$
4 $4: 1$
Mechanical Properties of Fluids

143092 Work done in increasing the size of a soap bubble from a radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ is nearly (surface tension of soap solution $=0.05 \mathrm{Nm}^{-1}$ )

1 $(0.70 \pi) \mathrm{mJ}$
2 $(0.64 \pi) \mathrm{mJ}$
3 $(0.30 \pi) \mathrm{mJ}$
4 $(0.58 \pi) \mathrm{mJ}$
Mechanical Properties of Fluids

143094 A water drop of radius $1 \mathrm{~cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be:
[Given $\pi=3.14$ ]

1 $8.5 \times 10^{-4} \mathrm{~J}$
2 $8.2 \times 10^{-4} \mathrm{~J}$
3 $7.5 \times 10^{-4} \mathrm{~J}$
4 $5.3 \times 10^{-4} \mathrm{~J}$
Mechanical Properties of Fluids

143095 A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 \times 10^{-4} \mathrm{Ncm}^{-1}$. The radius of drop in cm will be: (Take: $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $\frac{15}{\sqrt{2 \rho-\sigma}}$
2 $\frac{15}{\sqrt{\rho-\sigma}}$
3 $\frac{3}{2 \sqrt{\rho-\sigma}}$
4 $\frac{3}{20 \sqrt{2 \rho-\sigma}}$
Mechanical Properties of Fluids

143096 Two glasses with identical volumes are filled with water to the half - way mark and are kept side by side, two solid cubes made of the same metal are now dropped into the two glasses and both of them sink in the water. The first is glasses completely filled now. The second glass is still $\frac{7}{16}^{\text {th }}$ empty. The ratio of the surface areas of the cubes dropped into the first and the second glass is

1 $16: 7$
2 $8: 1$
3 $2: 1$
4 $4: 1$