A cylinder with a movable piston contains air under a pressure $p_1$ and a soap bubble of radius $'r'$ . The pressure $p_2$ to which the air should be compressed by slowly pushing the piston into the cylinder for the soap bubble to reduce its size by half will be: (The surface tension is $\sigma $ , and the temperature $T$ is maintained constant)
A cylinder with a movable piston contains air under a pressure $p_1$ and a soap bubble of radius $'r'$ . The pressure $p_2$ to which the air should be compressed by slowly pushing the piston into the cylinder for the soap bubble to reduce its size by half will be: (The surface tension is $\sigma $ , and the temperature $T$ is maintained constant)
- A
$\left[ {8{p_1} + \frac{{24\sigma }}{r}} \right]$
- B
$\left[ {4{p_1} + \frac{{24\sigma }}{r}} \right]$
- C
$\left[ {2{p_1} + \frac{{24\sigma }}{r}} \right]$
- D
$\left[ {2{p_1} + \frac{{12\sigma }}{r}} \right]$
Similar Questions
The adjoining diagram shows three soap bubbles $A, B$ and $C$ prepared by blowing the capillary tube fitted with stop cocks, $S_1$, $S_2$ and $S_3$. With stop cock $S$ closed and stop cocks $S_1$, $S_2$ and $S_3$ opened
The adjoining diagram shows three soap bubbles $A, B$ and $C$ prepared by blowing the capillary tube fitted with stop cocks, $S_1$, $S_2$ and $S_3$. With stop cock $S$ closed and stop cocks $S_1$, $S_2$ and $S_3$ opened
When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{{5r}}{4}$.Taking the atmospheric pressure to be equal to $10\,m$ height of water column, the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature)
When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{{5r}}{4}$.Taking the atmospheric pressure to be equal to $10\,m$ height of water column, the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature)
- [JEE MAIN 2018]
If two soap bubbles of different radii are connected by a tube,
If two soap bubbles of different radii are connected by a tube,
Formation of bubble are in Column - $\mathrm{I}$ and pressure difference between them are given in Column - $\mathrm{II}$. Match them appropriately.
Column - $\mathrm{I}$
Column - $\mathrm{II}$
$(a)$ Liquid drop in air
$(i)$ $\frac{{4T}}{R}$
$(b)$ Bubble of liquid in air
$(ii)$ $\frac{{2T}}{R}$
$(iii)$ $\frac{{2R}}{T}$
Formation of bubble are in Column - $\mathrm{I}$ and pressure difference between them are given in Column - $\mathrm{II}$. Match them appropriately.
| Column - $\mathrm{I}$ | Column - $\mathrm{II}$ |
| $(a)$ Liquid drop in air | $(i)$ $\frac{{4T}}{R}$ |
| $(b)$ Bubble of liquid in air | $(ii)$ $\frac{{2T}}{R}$ |
| $(iii)$ $\frac{{2R}}{T}$ |
Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is
Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is
- [KVPY 2018]