Question
The excess pressure inside a soap bubble is thrice the excess pressure inside a moving soap bubble. What is the ratio between the volume of the first and second bubble?
✓
Answer
Let r1 and r2 be the radii of soap bubbles, excess pressure in them are $\frac{4\sigma}{\text{r}_1}$ and $\frac{4\sigma}{\text{r}_2},$ where $\sigma$ is the surface tension. Given: $\text{P}_1=\text{3P}_2$
$\frac{4\sigma}{\text{r}_1}=3\frac{4\sigma}{\text{r}_2}$
$\therefore\text{r}_2=3\text{r}_1$
Volume fo first to second bubble,$=\frac{\text{r}_1^3}{\text{r}^3_2}=\frac{1}{3^3}=\frac{1}{27}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Figure shows a conducting circular loop of radius a placed in a uniform, perpendicular magnetic field B. A thick metal rod OA is pivoted at the centre O. The other end of the rod touches the loop at A. The centre O and a fixed point C on the loop are connected by a wire OC of resistance R. A force is applied at the middle point of the rod OA perpendicularly, so that the rod rotates clockwise at a uniform angular velocity $\omega.$ Find the force.
→
Two thermos flasks are of the same height and same capacity. One has a circular cross-section while the other has a square cross-section. Which of the two is better?
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
The 200m free style women's swimming gold medal at Seol Olympic 1988 went to Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57.56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.
These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.
The pressure of a gas changes linearly with volume from 10kPa, 200cc to 50kPa, 50cc.
- Calculate the work done by the gas.
- If no heat is supplied or extracted from the gas, what is the change in the internal energy of the gas?
The moment of inertia of two rotating bodies A and B are IA, and IB, (IA > IB) and their angular momentum are equal. Which of them has greater kinetic energy?
Two identical cylinders 'run a race' starting from rest at the top of an inclined plane, one slides without rolling and other rolls without slipping. Assuming that no mechanical energy is dissipated in heat, which one will win?
Two vectors have magnitudes 2m and 3m. The angle between them is 60°. Find:
- The scalar product of the two vectors.
- The magnitude of their vector product.
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
Do the intermediate states of the system (before settling to the final equilibrium state) lie on its P-V-T surface?
Do the intermediate states of the system (before settling to the final equilibrium state) lie on its P-V-T surface?