Two soap bubbles of radii R and r come in con | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The excess pressure inside a soap bubble of radius $r$ is given by $P = \frac{4S}{r}$,where $S$ is the surface tension.For the bubble with radius

Vedclass · Accepted Answer

$\frac{Rr}{R-r}$

Vedclass · Answer

(B) The excess pressure inside a soap bubble of radius $r$ is given by $P = \frac{4S}{r}$,where $S$ is the surface tension.For the bubble with radius $R$,the pressure inside is $P_1 = P_{atm} + \frac{4S}{R}$.For the bubble with radius $r$,the pressure inside is $P_2 = P_{atm} + \frac{4S}{r}$.Since $R > r$,the pressure $P_2$ is greater than $P_1$.The common surface will bulge towards the bubble with the larger radius $(R)$.The pressure difference across the common surface is $\Delta P = P_2 - P_1 = \frac{4S}{r} - \frac{4S}{R}$.Let $r_c$ be the radius of curvature of the common surface. Then $\Delta P = \frac{4S}{r_c}$.Equating the two expressions for $\Delta P$:$\frac{4S}{r_c} = 4S \left( \frac{1}{r} - \frac{1}{R} \right)$.$\frac{1}{r_c} = \frac{R - r}{Rr}$.Therefore,$r_c = \frac{Rr}{R - r}$.

Two soap bubbles of radii $R$ and $r$ come in contact. $R$ is more than $r$. The radius of curvature of the common surface is

Similar Questions

$1000$ droplets of water,each having a diameter of $2 \ mm$,coalesce to form a single drop. Given the surface tension of water is $0.072 \ N/m$. The energy loss in the process is

The excess pressure inside a first spherical drop of water is three times that of a second spherical drop of water. Then the ratio of the mass of the first spherical drop to that of the second spherical drop is

Pressure inside two soap bubbles are $1.01 \, atm$ and $1.02 \, atm$. The ratio between their volumes is:

$216$ small identical liquid drops,each of surface area $A$,coalesce to form a bigger drop. If the surface tension of the liquid is $T$,what is the energy released in the process (in $AT$)?

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is

Vedclass Test Series

Exam Paper Generator

Online Exam Module