Excess Pressure in Bubbles

Q.

A soap bubble is given a negative charge, then its radius

Q. A soap bubble in vacuum has a radius $3\text{cm}$ and another soap bubble in vacuum has a radius $4\text{cm}$. If both bubbles coalesce under isothermal condition, then the radius of the new bubble will be

1. $6\text{cm}$
2. $5\text{cm}$
3. $4\text{cm}$
4. $3\text{cm}$

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

1. $5\text{cm}$
2. $8\text{cm}$
3. $1\text{cm}$
4. $3\text{cm}$

Q. there are two concentric conducting shells. the potential of outer shell is 10V and that of inner shell is 15V. if the outer shell is grounded the potential of inner shell is ?

Q.

What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature $\left({20}^{\circ }C\right)$ is $2.50\times {10}^{–2}N{m}^{–1}$? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is $1.01\times {10}^{5}Pa)$.

Q. There is a horizontal film of soap solution on it a thread is placed in form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius R. If the surface tension of the soap solution is T, then the tension in the loop will be

1. 
2. 
3. 
4. 

Q. If more air is pushed in a soap bubble, the pressure in it

1. decreases
2. increases
3. remains same
4. becomes zero

Q.

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius with the bottom of the vessel. If r << R and the surface tension of water is T, the value of r just before bubbles detach is (density of water is ${\rho }_w$).

1. $R^2\sqrt{\frac{{\rho }_{w}g}{T}}$

2. $R^2\sqrt{\frac{2{\rho }_{w}g}{3T}}$

3. $R^2\sqrt{\frac{3{\rho }_{w}g}{T}}$

4. $R^2\sqrt{\frac{{\rho }_{w}g}{6T}}$

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

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. A spherical drop of water has $1\text{mm}$ radius. If the surface tension of water is $75\times {10}^{-3}\text{N/m}$, then the difference in pressure between the inside and outside of the drop is

1. $35{\text{N/m}}^2$
2. $70{\text{N/m}}^2$
3. $140{\text{N/m}}^2$
4. $150{\text{N/m}}^2$

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. The excess pressure inside the first soap bubble is three times that inside the second bubble. Then, the ratio of the volume of the first bubble to that of the second bubble will be

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

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. There is a small hole in a hollow sphere. The water enters into it when it is taken to a depth of $40\text{cm}$ under water. The surface tension of water is $0.07\text{N/m}$. The diameter of the hole is
[Take $g=10{\text{m/s}}^2$]

1. $7\text{mm}$
2. $0.07\text{mm}$
3. $0.7\text{mm}$
4. $0.007\text{mm}$

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.

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? Surface tension of mercury at that temperature $\left({20}^{\circ }C\right)$ is $4.65\times {10}^{–1}N{m}^{–1}$ . The atmospheric pressure is $1.01\times {10}^5$ Pa. Also give the excess pressure inside the drop.

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.

Water is flowing in streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level.

1. The pressures at A and B are equal for any shape of the tube.

2. The pressures are never equal.

3. The pressures are equal if the tube has a uniform cross section.

4. The pressures may be equal even if the tube has a non-uniform cross section.

Q. If difference of pressure between inside and outside of the spherical drop is $70{\text{N/m}}^2$, then what is the radius of spherical drop ?
Given: Surface tension of water is $70\times {10}^{-3}\text{N/m}$.

1. $1\text{mm}$
2. $2\text{mm}$
3. $0.1\text{mm}$
4. $0.2\text{mm}$

Q. The surface tension of water in contact with air at ${18}^{\circ }\text{C}$ is $0.073\text{N/m}$. The pressure inside a droplet of water is to be $0.02{\text{N/cm}}^2$ greater than the outside pressure. Calculate the diameter of the droplet of water.

1. $1.47\text{mm}$
2. $0.73\text{mm}$
3. $1.45\text{mm}$
4. $1.46\text{mm}$

Q. Two soap bubbles in vacuum having radii $3\text{cm}$ and $4\text{cm}$ respectively coalesce under isothermal conditions to form a single bubble. Then the radius of the new bubble in $cm$ is

Q. A steel wire having a radius of $2.0mm$, carrying a load of $4kg$, is hanging from a ceiling. Given that $g=3.1\pi m{s}^{-2}$, what will be the tensile stress that would be developed in the wire?

1. $4.8\times {10}^{6}N{m}^{-2}$
2. $5.2\times {10}^{6}N{m}^{-2}$
3. $6.2\times {10}^{6}N{m}^{-2}$
4. $3.1\times {10}^{6}N{m}^{-2}$

Q. If the excess pressure inside a soap bubble of radius $1\text{cm}$ is balanced by an oil
($\rho =0.8{\text{g/cm}}^3)$ column of height $2\text{mm}$, then the surface tension of soap solution will be
[Take $g=10{\text{m/s}}^2$]

1. $0.02\text{N/m}$
2. $0.04\text{N/m}$
3. $0.09\text{N/m}$
4. $0.08\text{N/m}$

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

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 bubble of air has radius $0.2\text{mm}$ in water. If the bubble had been formed $20\text{cm}$ below the water surface on a day when the atmospheric pressure was $1.013\times {10}^5\text{Pa}$, then what would have been the total pressure inside the bubble? (surface tension of water = $73\times {10}^{-3}\text{N/m}$)

1. $1.052\times {10}^5\text{Pa}$
2. $1.039\times {10}^5\text{Pa}$
3. $1.152\times {10}^5\text{Pa}$
4. $1.022\times {10}^5\text{Pa}$

Q.

Find the increase in pressure required to decrease the volume of a water sample by $0.01\%$. Bulk modulus of water = $2.1\times {10}^{9}N{m}^{-2}$

Q. A ray of light travelling in glass medium $({\mu }_g=\frac{3}{2})$ is incident on a horizontal glass-air interface at the critical angle ${\theta }_c$. If a thin layer of water $({\mu }_w=\frac{4}{3})$ is now poured on the glass-air interface , then the angle at which the ray of light emerges into water at glass-water surface will be

1. ${\sin }^{-1}(\frac{3}{4})$
2. ${\sin }^{-1}(\frac{3}{5})$
3. ${\cos }^{-1}(\frac{3}{4})$
4. ${\cos }^{-1}(\frac{3}{5})$

Q. Two soap bubbles are blown. In first bubble, excess pressure is $4$ times that of second bubble. The ratio of the radii of first and second soap bubble is

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