A soap bubble, blown by a mechanical pump at | vedclass

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

Question

(D) Let the volume of the soap bubble be $V$ and the rate of increase be constant, so $V = kt$, where $k$ is a constant.Since $V = \frac{4}{3}\pi R^3$

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Let the volume of the soap bubble be $V$ and the rate of increase be constant, so $V = kt$, where $k$ is a constant.Since $V = \frac{4}{3}\pi R^3$, we have $\frac{4}{3}\pi R^3 = kt$, which implies $R = \left( \frac{3k}{4\pi} t \right)^{1/3}$.The pressure inside a soap bubble is given by $P_{in} = P_{atm} + \frac{4T}{R}$, where $P_{atm}$ is atmospheric pressure and $T$ is surface tension.Substituting $R$ in the pressure equation: $P_{in} = P_{atm} + \frac{4T}{\left( \frac{3k}{4\pi} t \right)^{1/3}}$.This can be written as $P_{in} = P_{atm} + C \cdot t^{-1/3}$, where $C$ is a constant.None of the provided graphs ($P$ vs $1/t$, $P$ vs $\log(t)$, or $P$ vs $t$) represent the relationship $P \propto t^{-1/3}$.Therefore, the correct option is $D$.

$A$ soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by

Similar Questions

Write the equation of excess pressure (pressure difference) for a bubble in air and a bubble in water.

$A$ soap bubble $(S.T = 30\, dyne/cm)$ has a radius of $1\, cm$. The work done in doubling its radius would be ........ $ergs$.

$A$ spherical drop of water has a radius of $1\, mm$. If the surface tension of water is $70 \times 10^{-3}\, N/m$,the difference of pressure between the inside and outside of the spherical drop is ........ $N/m^2$.

$64$ small mercury droplets,each of radius $r$ and charge $q$,coalesce to form a single large drop. What is the ratio of the surface charge density of a small droplet to that of the large drop?

There is a small hole in a hollow sphere. Water enters the sphere when it is taken to a depth of $40 \, cm$ in water. The diameter of the hole is ....... $mm$ (Surface tension of water $= 0.07 \, N/m$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module