Excess Pressure in Bubbles

Q. Two soap bubbles of radii $4\text{cm}$ and $5\text{cm}$ are touching each other over a common surface $S_1{S}_2$ (shown in figure). Then, radius of the common surface will be

1. $12\text{cm}$
2. $20\text{cm}$
3. $16\text{cm}$
4. $10\text{cm}$

Q. A soap bubble of radius $R$ is surrounded by another soap bubble of radius $2R$ as shown. Taking surface tension = $S$, the pressure inside the smaller soap bubble, in excess of the atmospheric pressure will be

1. $\frac{4S}{4}$
2. $\frac{3S}{4}$
3. $\frac{6S}{4}$
4. None of these

Q. The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is:

1. $1:9$
2. $1:3$
3. $3:1$
4. $1:27$

Q. What should be the pressure inside a air bubble of radius $0.1\text{mm}$ situated $1\text{m}$ below the water surface?
(Take surface tension of water $T=7.2\times {10}^{-2}\text{N/m}$ and $g=10{\text{m/s}}^2$)

1. $3.5\times {10}^5\text{Pa}$
2. $1.11\times {10}^5\text{Pa}$
3. $2.11\times {10}^5\text{Pa}$
4. $3\times {10}^5\text{Pa}$

Q. A soap bubble of diameter $8\text{mm}$ is formed in air. If the surface tension of liquid is $30\text{dyne/cm}$, then excess pressure inside the soap bubble is

1. $150{\text{dyne/cm}}^2$
2. $300{\text{dyne/cm}}^2$
3. $3\times {10}^{-3}{\text{dyne/cm}}^2$
4. $12{\text{dyne/cm}}^2$

Q. A soap bubble of diameter $10\text{mm}$ has an excess pressure of $50{\text{N/m}}^2$. Find the surface tension of soap solution.

1. $0.31\text{N/m}$
2. $0.063\text{N/m}$
3. $0.063{\text{N/m}}^2$
4. $0.031{\text{N/m}}^2$

Q.

A cubical tank of side $3.0m$is evacuated of air. That is, the number of molecules of air inside the tank is insignificant compared to the number in the same volume outside. The atmospheric pressure is ${10}^{5}Pa$. What is the crushing force exerted by the atmosphere on the tank?

Q. A spherical soap bubble of radius $1\text{cm}$ is formed inside another of radius $3\text{cm}$. The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is

1. $1.33\text{cm}$
2. $0.75\text{cm}$
3. $7.5\text{cm}$
4. $13.3\text{cm}$

Q.

An air bubble in sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If _am_g = 1.5, the distance of bubble from refracting surface is

[CPMT 2002]

1. 1.2 cm

2. 3.2 cm

3. 2.8 cm

4. 1.6 cm

Q. What will be the diameter (in $\text{mm}$) of a water droplet, the pressure inside which is $0.05{\text{N/cm}}^2$ greater than the outside pressure? (Take surface tension as $0.075\text{N/m}$).

1. $3$
2. $0.3$
3. $0.6$
4. $6$

Q. The excess pressure inside a spherical drop of water is four times that of another water drop. Then the mass ratio of the two drops is

1. $1:16$
2. $1:64$
3. $1:4$
4. $1:8$

Q. Pressure inside two soap bubbles of a liquid solution are $1.01\text{atm}$ and $1.02\text{atm}$. Ratio of their volume is

1. $4:1$
2. $8:1$
3. $1:8$
4. $1:4$

Q. A water droplet splits into $27$ identical small droplets. The pressure difference between the inner and outer surface of the big droplet will be

1. Same as that of smaller droplet
2. $1/3\text{rd}$ of the pressure difference for smaller droplet.
3. $1/4\text{th}$ of the pressure difference for smaller droplet.
4. None of these

Q. Shown in the figure, is a hollow ice-cream cone (it is open at the top). If its mass is $M$, radius of its top is $R$ and height $H$ then, its moment of inertia about its axis is:

1. $\frac{M{R}^2}{3}$
2. $\frac{M{R}^2}{2}$
3. $\frac{M(R^2+H^2)}{4}$
4. $\frac{M{H}^2}{3}$

Q. Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure $8N/m^2.$ The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio $n_B/n_A$, where $n_A$ and $n_B$ are the number of moles of air in bubbles A and B, respectively.
Given that for a gas, the relation between number of moles and pressure and volume is PV = kn, where k is constant at a particular temperature.
(IIT-JEE-2009)
[Neglect the effect of gravity.]

1. 6
2. 7
3. 8
4. 9

Q. A beaker is filled with liquid solution. A soap bubble of radius $1\text{mm}$ is formed in the bulk of liquid solution. If surface tension of liquid is $1.6\text{N/m}$, find the excess pressure inside the soap bubble.

1. $1.6\times {10}^3{\text{N/m}}^2$
2. $3.2\times {10}^3{\text{N/m}}^2$
3. $0.8\times {10}^{-3}{\text{N/m}}^2$
4. None of these

Q. A soap bubble having radius $1mm$ is blown from a detergent solution having a surface tension of $2.5\times {10}^{-2}N/m$. The pressure inside the bubble is equal to the pressure at a point which is $Z_0$ below the free surface of water in a container. Find the value of $Z_0$ . Taking $g=10m/s^2$, density of water = ${10}^{3}kg/m^3$

1. $100cm$
2. $10cm$
3. $1cm$
4. $0.5cm$

Q. A spherical drop of water has radius $r\text{m}$. If surface tension of water is $70\times {10}^{-3}\text{N/m}$ and the pressure difference between inside and outside of the spherical drop is $280{\text{N/m}}^2$. Find the value of $r$.

1. $1\text{mm}$
2. $0.5\text{mm}$
3. $0.4\text{mm}$
4. $0.2\text{mm}$

Q. A beaker is filled with liquid having surface tension $0.07\text{N/m}$. If a bubble of radius $0.5\text{mm}$ is formed at depth $h=1\text{m}$ below the free surface, then find difference between the pressure acting inside the bubble and free surface.
(Density of liquid is $1000{\text{kg /m}}^3)$

1. $0.28\times {10}^4{\text{N/m}}^2$
2. $0.56\times {10}^4{\text{N/m}}^2$
3. $1.028\times {10}^4{\text{N/m}}^2$
4. $2.014\times {10}^4{\text{N/m}}^2$