Advertisements
Advertisements
Question
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
Options
4
2
1
0.125
Solution
Let the excess pressure inside the second bubble be P.
∴ Excess pressure inside the first bubble = 2P
Let the radius of the second bubble be R.
Let the radius of the first bubble be x.
\[\text{ Excess pressure inside the 2 nd soap bubble :} \]
\[P = \frac{4S}{R} . . . (1)\]
\[\text{ Excess pressure inside the 1st soap bubble: }\]
\[2P = \frac{4S}{x}\]
\[\text{ From (1), we get :} \]
\[2\left( \frac{4S}{R} \right) = \frac{4S}{x}\]
\[ \Rightarrow x = \frac{R}{2}\]
\[\text{ Volume of the first bubble }= \frac{4}{3} \pi x^3 \]
\[\text{ Volume of the second bubble } = \frac{4}{3} \pi R^3 \]
\[ \Rightarrow \frac{4}{3} \pi x^3 = n\frac{4}{3} \pi R^3 \]
\[ \Rightarrow x^3 = {nR}^3 \]
\[ \Rightarrow \left( \frac{R}{2} \right)^3 = {nR}^3 \]
\[ \Rightarrow n = \frac{1}{8} = 0 . 125\]
APPEARS IN
RELATED QUESTIONS
A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
The total energy of free surface of a liquid drop is 2π times the surface tension of the liquid. What is the diameter of the drop? (Assume all terms in SI unit).
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)
Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is 30 dyne/cm. (Π = 3.142).
The contact angle between pure water and pure silver is 90°. If a capillary tube made of silver is dipped at one end in pure water, will the water rise in the capillary?
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
If two soap bubbles of different radii are connected by a tube,
A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension the the thread. Surface tension of soap solution = 0.030 N m−1.
Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?
A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.
Derive an expression for capillary rise for a liquid having a concave meniscus.
Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7 × 10-2 N/m. The angle of contact between water and glass is zero, the density of water = 1000 kg/m3, g = 9.8 m/s2.
Water rises to a height of 20 mm in a capillary tube. If the radius made 1/3rd of its previous value, to what height will the water now rise in the tube?
Two soap bubbles have a radius in the ratio of 2:3. Compare the works done in blowing these bubbles.
Define the surface tension of a liquid.
A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is ______.
The surface tension of a soap solution is T. The work done in blowing a soap bubble of diameter d to that of a diameter 2d is ______.
Find the work done when a drop of mercury of radius 2 mm breaks into 8 equal droplets. [Surface tension of mercury = 0.4855 J/m2].
Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.
