01. Surface Tension and Surface Energy
Mechanical Properties of Fluids

142807 A ring of radius $R$ is kept on water surface.
Surface tension of water is $T$ and mass is $\mathbf{m}$. What force required to lift the ring from water surface?

1 $(\mathrm{mg}+2 \mathrm{~T} \pi \mathrm{R})$
2 $(2 \mathrm{mg}+\pi \mathrm{R})$
3 $(3 \mathrm{mg}+2 \pi \mathrm{TR})$
4 $(\mathrm{mg}+4 \mathrm{~T} \pi \mathrm{R})$
Mechanical Properties of Fluids

142808 A hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. If outer diameter and the density of the bowl are $1 \mathrm{~m}$ and $2 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$ respectively, then the inner diameter of the bowl will be

1 $0.94 \mathrm{~m}$
2 $0.97 \mathrm{~m}$
3 $0.98 \mathrm{~m}$
4 $0.99 \mathrm{~m}$
Mechanical Properties of Fluids

142812 Work of 3.0 $\times 10^{-4}$ joule is required to be done in increasing the size of a soap film from $10 \mathrm{~cm} \times$ $6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$. The surface tension of the film is

1 $5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
2 $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
3 $1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
4 $1.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
Mechanical Properties of Fluids

142816 A mercury drop of radius $1 \mathrm{~cm}$ is sprayed into $10^{6}$ drops of equal size. The energy expressed in joule is (surface tension of Mercury is $460 \times 10^{-3}$ $\mathbf{N} / \mathbf{m})$

1 0.057
2 5.7
3 $5.7 \times 10^{-4}$
4 $5.7 \times 10^{-6}$
Mechanical Properties of Fluids

142807 A ring of radius $R$ is kept on water surface.
Surface tension of water is $T$ and mass is $\mathbf{m}$. What force required to lift the ring from water surface?

1 $(\mathrm{mg}+2 \mathrm{~T} \pi \mathrm{R})$
2 $(2 \mathrm{mg}+\pi \mathrm{R})$
3 $(3 \mathrm{mg}+2 \pi \mathrm{TR})$
4 $(\mathrm{mg}+4 \mathrm{~T} \pi \mathrm{R})$
Mechanical Properties of Fluids

142808 A hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. If outer diameter and the density of the bowl are $1 \mathrm{~m}$ and $2 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$ respectively, then the inner diameter of the bowl will be

1 $0.94 \mathrm{~m}$
2 $0.97 \mathrm{~m}$
3 $0.98 \mathrm{~m}$
4 $0.99 \mathrm{~m}$
Mechanical Properties of Fluids

142812 Work of 3.0 $\times 10^{-4}$ joule is required to be done in increasing the size of a soap film from $10 \mathrm{~cm} \times$ $6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$. The surface tension of the film is

1 $5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
2 $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
3 $1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
4 $1.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
Mechanical Properties of Fluids

142816 A mercury drop of radius $1 \mathrm{~cm}$ is sprayed into $10^{6}$ drops of equal size. The energy expressed in joule is (surface tension of Mercury is $460 \times 10^{-3}$ $\mathbf{N} / \mathbf{m})$

1 0.057
2 5.7
3 $5.7 \times 10^{-4}$
4 $5.7 \times 10^{-6}$
Mechanical Properties of Fluids

142807 A ring of radius $R$ is kept on water surface.
Surface tension of water is $T$ and mass is $\mathbf{m}$. What force required to lift the ring from water surface?

1 $(\mathrm{mg}+2 \mathrm{~T} \pi \mathrm{R})$
2 $(2 \mathrm{mg}+\pi \mathrm{R})$
3 $(3 \mathrm{mg}+2 \pi \mathrm{TR})$
4 $(\mathrm{mg}+4 \mathrm{~T} \pi \mathrm{R})$
Mechanical Properties of Fluids

142808 A hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. If outer diameter and the density of the bowl are $1 \mathrm{~m}$ and $2 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$ respectively, then the inner diameter of the bowl will be

1 $0.94 \mathrm{~m}$
2 $0.97 \mathrm{~m}$
3 $0.98 \mathrm{~m}$
4 $0.99 \mathrm{~m}$
Mechanical Properties of Fluids

142812 Work of 3.0 $\times 10^{-4}$ joule is required to be done in increasing the size of a soap film from $10 \mathrm{~cm} \times$ $6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$. The surface tension of the film is

1 $5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
2 $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
3 $1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
4 $1.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
Mechanical Properties of Fluids

142816 A mercury drop of radius $1 \mathrm{~cm}$ is sprayed into $10^{6}$ drops of equal size. The energy expressed in joule is (surface tension of Mercury is $460 \times 10^{-3}$ $\mathbf{N} / \mathbf{m})$

1 0.057
2 5.7
3 $5.7 \times 10^{-4}$
4 $5.7 \times 10^{-6}$
Mechanical Properties of Fluids

142807 A ring of radius $R$ is kept on water surface.
Surface tension of water is $T$ and mass is $\mathbf{m}$. What force required to lift the ring from water surface?

1 $(\mathrm{mg}+2 \mathrm{~T} \pi \mathrm{R})$
2 $(2 \mathrm{mg}+\pi \mathrm{R})$
3 $(3 \mathrm{mg}+2 \pi \mathrm{TR})$
4 $(\mathrm{mg}+4 \mathrm{~T} \pi \mathrm{R})$
Mechanical Properties of Fluids

142808 A hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. If outer diameter and the density of the bowl are $1 \mathrm{~m}$ and $2 \times 10^{4} \mathrm{~kg} / \mathrm{m}^{3}$ respectively, then the inner diameter of the bowl will be

1 $0.94 \mathrm{~m}$
2 $0.97 \mathrm{~m}$
3 $0.98 \mathrm{~m}$
4 $0.99 \mathrm{~m}$
Mechanical Properties of Fluids

142812 Work of 3.0 $\times 10^{-4}$ joule is required to be done in increasing the size of a soap film from $10 \mathrm{~cm} \times$ $6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$. The surface tension of the film is

1 $5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
2 $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
3 $1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
4 $1.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$
Mechanical Properties of Fluids

142816 A mercury drop of radius $1 \mathrm{~cm}$ is sprayed into $10^{6}$ drops of equal size. The energy expressed in joule is (surface tension of Mercury is $460 \times 10^{-3}$ $\mathbf{N} / \mathbf{m})$

1 0.057
2 5.7
3 $5.7 \times 10^{-4}$
4 $5.7 \times 10^{-6}$