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
Advertisements
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
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Define the angle of contact.
Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
By a surface of a liquid we mean
The capillaries shown in figure have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10−2 N m−1.
Consider an ice cube of edge 1.0 cm kept in a gravity-free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water.
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
The surface tension of a liquid at critical temperature is ______
What will be the shape of the liquid meniscus for the obtuse angle of contact?
How does the friction arise between the surfaces of two bodies in relative motion?
What is capillarity?
Water rises upto a height h in a capillary tube on the surface of the earth. The value of h will increase, if the experimental setup is kept in [g = acceleration due to gravity]
A large number of liquid drops each of radius 'r' coalesce to form a big drop of radius 'R'. The energy released in the process in converted into kinetic energy of the big drop. The speed of the big drop is ______. (T = surface tension of liquid, p = density of liquid)
The sufrace tension and vapour pressure of water at 20°C is 7.28 × 10–2 Nm–1 and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20°C?
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pully as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is ______.
The surface tension of soap solution is 25 × 10-3 Nm-1. The excess of pressure inside a soap bubble of diameter 1 cm is ______.
The surface tension of boiling water is ______.
