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

143023 The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is :

1 2
2 4
3 6
4 8
5 16
Mechanical Properties of Fluids

143024 A soap bubble in air (two surfaces) has surface tension $0.03 \mathrm{Nm}^{-1}$. Find the gauge pressure inside a bubble of diameter $30 \mathrm{~mm}$.

1 $2 \mathrm{~Pa}$
2 $4 \mathrm{~Pa}$
3 $16 \mathrm{~Pa}$
4 $10 \mathrm{~Pa}$
5 $8 \mathrm{~Pa}$
Mechanical Properties of Fluids

143025 The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is
( $\varepsilon_{0}=$ permittivity of the free space)

1 $\sqrt{\frac{\mathrm{Sr}}{8 \varepsilon_{0}}}$
2 $\sqrt{\frac{\mathrm{Sr}}{4 \varepsilon_{0}}}$
3 $\sqrt{\frac{4 \mathrm{Sr}}{\varepsilon_{0}}}$
4 $\sqrt{\frac{8 \mathrm{Sr}}{\varepsilon_{0}}}$
Mechanical Properties of Fluids

143026 When a soap bubble of radius $0.2 \mathrm{~mm}$ is charged, it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^{2}}{2 \varepsilon_{0}}$, where $\sigma$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure, then the surface tension of the soap solution is
$\left(\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)$

1 $8.85 \times 10^{-4} \mathrm{Nm}^{-1}$
2 $12.4 \times 10^{-4} \mathrm{Nm}^{-1}$
3 $11.3 \times 10^{-4} \mathrm{Nm}^{-1}$
4 $90 \times 10^{-4} \mathrm{Nm}^{-1}$
Mechanical Properties of Fluids

143023 The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is :

1 2
2 4
3 6
4 8
5 16
Mechanical Properties of Fluids

143024 A soap bubble in air (two surfaces) has surface tension $0.03 \mathrm{Nm}^{-1}$. Find the gauge pressure inside a bubble of diameter $30 \mathrm{~mm}$.

1 $2 \mathrm{~Pa}$
2 $4 \mathrm{~Pa}$
3 $16 \mathrm{~Pa}$
4 $10 \mathrm{~Pa}$
5 $8 \mathrm{~Pa}$
Mechanical Properties of Fluids

143025 The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is
( $\varepsilon_{0}=$ permittivity of the free space)

1 $\sqrt{\frac{\mathrm{Sr}}{8 \varepsilon_{0}}}$
2 $\sqrt{\frac{\mathrm{Sr}}{4 \varepsilon_{0}}}$
3 $\sqrt{\frac{4 \mathrm{Sr}}{\varepsilon_{0}}}$
4 $\sqrt{\frac{8 \mathrm{Sr}}{\varepsilon_{0}}}$
Mechanical Properties of Fluids

143026 When a soap bubble of radius $0.2 \mathrm{~mm}$ is charged, it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^{2}}{2 \varepsilon_{0}}$, where $\sigma$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure, then the surface tension of the soap solution is
$\left(\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)$

1 $8.85 \times 10^{-4} \mathrm{Nm}^{-1}$
2 $12.4 \times 10^{-4} \mathrm{Nm}^{-1}$
3 $11.3 \times 10^{-4} \mathrm{Nm}^{-1}$
4 $90 \times 10^{-4} \mathrm{Nm}^{-1}$
Mechanical Properties of Fluids

143023 The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is :

1 2
2 4
3 6
4 8
5 16
Mechanical Properties of Fluids

143024 A soap bubble in air (two surfaces) has surface tension $0.03 \mathrm{Nm}^{-1}$. Find the gauge pressure inside a bubble of diameter $30 \mathrm{~mm}$.

1 $2 \mathrm{~Pa}$
2 $4 \mathrm{~Pa}$
3 $16 \mathrm{~Pa}$
4 $10 \mathrm{~Pa}$
5 $8 \mathrm{~Pa}$
Mechanical Properties of Fluids

143025 The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is
( $\varepsilon_{0}=$ permittivity of the free space)

1 $\sqrt{\frac{\mathrm{Sr}}{8 \varepsilon_{0}}}$
2 $\sqrt{\frac{\mathrm{Sr}}{4 \varepsilon_{0}}}$
3 $\sqrt{\frac{4 \mathrm{Sr}}{\varepsilon_{0}}}$
4 $\sqrt{\frac{8 \mathrm{Sr}}{\varepsilon_{0}}}$
Mechanical Properties of Fluids

143026 When a soap bubble of radius $0.2 \mathrm{~mm}$ is charged, it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^{2}}{2 \varepsilon_{0}}$, where $\sigma$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure, then the surface tension of the soap solution is
$\left(\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)$

1 $8.85 \times 10^{-4} \mathrm{Nm}^{-1}$
2 $12.4 \times 10^{-4} \mathrm{Nm}^{-1}$
3 $11.3 \times 10^{-4} \mathrm{Nm}^{-1}$
4 $90 \times 10^{-4} \mathrm{Nm}^{-1}$
Mechanical Properties of Fluids

143023 The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is :

1 2
2 4
3 6
4 8
5 16
Mechanical Properties of Fluids

143024 A soap bubble in air (two surfaces) has surface tension $0.03 \mathrm{Nm}^{-1}$. Find the gauge pressure inside a bubble of diameter $30 \mathrm{~mm}$.

1 $2 \mathrm{~Pa}$
2 $4 \mathrm{~Pa}$
3 $16 \mathrm{~Pa}$
4 $10 \mathrm{~Pa}$
5 $8 \mathrm{~Pa}$
Mechanical Properties of Fluids

143025 The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is
( $\varepsilon_{0}=$ permittivity of the free space)

1 $\sqrt{\frac{\mathrm{Sr}}{8 \varepsilon_{0}}}$
2 $\sqrt{\frac{\mathrm{Sr}}{4 \varepsilon_{0}}}$
3 $\sqrt{\frac{4 \mathrm{Sr}}{\varepsilon_{0}}}$
4 $\sqrt{\frac{8 \mathrm{Sr}}{\varepsilon_{0}}}$
Mechanical Properties of Fluids

143026 When a soap bubble of radius $0.2 \mathrm{~mm}$ is charged, it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^{2}}{2 \varepsilon_{0}}$, where $\sigma$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure, then the surface tension of the soap solution is
$\left(\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)$

1 $8.85 \times 10^{-4} \mathrm{Nm}^{-1}$
2 $12.4 \times 10^{-4} \mathrm{Nm}^{-1}$
3 $11.3 \times 10^{-4} \mathrm{Nm}^{-1}$
4 $90 \times 10^{-4} \mathrm{Nm}^{-1}$