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

143106 A soap bubble of diameter a is produced using the soap solution of surface tension $T$. Find the energy required to double the radius of the bubble without change of temperature.

1 $2 \pi \mathrm{a}^{2} \mathrm{~T}$
2 $6 \pi \mathrm{a}^{2} \mathrm{~T}$
3 $3 \pi \mathrm{a}^{2} \mathrm{~T}$
4 $12 \pi \mathrm{a}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143107 What should be the pressure inside a small air bubble of $0.1 \mathrm{~mm}$ radius situated just below the water surface? Surface tension of water $=$ $7.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ and atmospheric pressure $=$ $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

1 $2.012 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.012 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
3 $1.027 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.027 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143108 Two rain drops reach the earth with their terminal velocities in the ratio $4: 9$. The ratio of their redii is:

1 $4: 9$
2 $2: 3$
3 $3: 2$
4 $9: 4$
Mechanical Properties of Fluids

143109 The pressures inside two soap bubbles are 1.01 and 1.02 atmospheres respectively. The ratio of their respective volumes is:

1 16
2 8
3 4
4 2
Mechanical Properties of Fluids

143106 A soap bubble of diameter a is produced using the soap solution of surface tension $T$. Find the energy required to double the radius of the bubble without change of temperature.

1 $2 \pi \mathrm{a}^{2} \mathrm{~T}$
2 $6 \pi \mathrm{a}^{2} \mathrm{~T}$
3 $3 \pi \mathrm{a}^{2} \mathrm{~T}$
4 $12 \pi \mathrm{a}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143107 What should be the pressure inside a small air bubble of $0.1 \mathrm{~mm}$ radius situated just below the water surface? Surface tension of water $=$ $7.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ and atmospheric pressure $=$ $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

1 $2.012 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.012 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
3 $1.027 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.027 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143108 Two rain drops reach the earth with their terminal velocities in the ratio $4: 9$. The ratio of their redii is:

1 $4: 9$
2 $2: 3$
3 $3: 2$
4 $9: 4$
Mechanical Properties of Fluids

143109 The pressures inside two soap bubbles are 1.01 and 1.02 atmospheres respectively. The ratio of their respective volumes is:

1 16
2 8
3 4
4 2
Mechanical Properties of Fluids

143106 A soap bubble of diameter a is produced using the soap solution of surface tension $T$. Find the energy required to double the radius of the bubble without change of temperature.

1 $2 \pi \mathrm{a}^{2} \mathrm{~T}$
2 $6 \pi \mathrm{a}^{2} \mathrm{~T}$
3 $3 \pi \mathrm{a}^{2} \mathrm{~T}$
4 $12 \pi \mathrm{a}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143107 What should be the pressure inside a small air bubble of $0.1 \mathrm{~mm}$ radius situated just below the water surface? Surface tension of water $=$ $7.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ and atmospheric pressure $=$ $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

1 $2.012 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.012 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
3 $1.027 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.027 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143108 Two rain drops reach the earth with their terminal velocities in the ratio $4: 9$. The ratio of their redii is:

1 $4: 9$
2 $2: 3$
3 $3: 2$
4 $9: 4$
Mechanical Properties of Fluids

143109 The pressures inside two soap bubbles are 1.01 and 1.02 atmospheres respectively. The ratio of their respective volumes is:

1 16
2 8
3 4
4 2
Mechanical Properties of Fluids

143106 A soap bubble of diameter a is produced using the soap solution of surface tension $T$. Find the energy required to double the radius of the bubble without change of temperature.

1 $2 \pi \mathrm{a}^{2} \mathrm{~T}$
2 $6 \pi \mathrm{a}^{2} \mathrm{~T}$
3 $3 \pi \mathrm{a}^{2} \mathrm{~T}$
4 $12 \pi \mathrm{a}^{2} \mathrm{~T}$
Mechanical Properties of Fluids

143107 What should be the pressure inside a small air bubble of $0.1 \mathrm{~mm}$ radius situated just below the water surface? Surface tension of water $=$ $7.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ and atmospheric pressure $=$ $1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

1 $2.012 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.012 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
3 $1.027 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.027 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Fluids

143108 Two rain drops reach the earth with their terminal velocities in the ratio $4: 9$. The ratio of their redii is:

1 $4: 9$
2 $2: 3$
3 $3: 2$
4 $9: 4$
Mechanical Properties of Fluids

143109 The pressures inside two soap bubbles are 1.01 and 1.02 atmospheres respectively. The ratio of their respective volumes is:

1 16
2 8
3 4
4 2