The excess pressure inside the first soap bub | vedclass

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

Question

(D) The excess pressure $P$ inside a soap bubble of radius $R$ is given by $P = \frac{4T}{R}$,where $T$ is the surface tension of the soap solution.Gi

Vedclass · Accepted Answer

$1: 8$

Vedclass · Answer

(D) The excess pressure $P$ inside a soap bubble of radius $R$ is given by $P = \frac{4T}{R}$,where $T$ is the surface tension of the soap solution.Given that the excess pressure in the first bubble $(P_{1})$ is twice that of the second bubble $(P_{2})$,we have $P_{1} = 2P_{2}$.Substituting the formula for excess pressure: $\frac{4T}{R_{1}} = 2 	imes \frac{4T}{R_{2}}$.Simplifying this,we get $\frac{1}{R_{1}} = \frac{2}{R_{2}}$,which implies $\frac{R_{2}}{R_{1}} = 2$ or $R_{2} = 2R_{1}$.The volume $V$ of a spherical bubble is given by $V = \frac{4}{3} \pi R^{3}$.The ratio of the volumes is $\frac{V_{1}}{V_{2}} = \frac{\frac{4}{3} \pi R_{1}^{3}}{\frac{4}{3} \pi R_{2}^{3}} = \left( \frac{R_{1}}{R_{2}} ight)^{3}$.Since $\frac{R_{1}}{R_{2}} = \frac{1}{2}$,the ratio of volumes is $\left( \frac{1}{2} ight)^{3} = \frac{1}{8}$.

The excess pressure inside the first soap bubble of radius $R_{1}$ is two times that inside the second soap bubble of radius $R_{2}$. The ratio of the volumes of the first bubble to that of the second bubble is:

Similar Questions

If two soap bubbles of equal radii $r$ coalesce,then the radius of curvature of the interface between the two bubbles will be:

$A$ big drop of radius $R$ is formed by $1000$ small droplets of water. The radius of each small droplet is:

When a big drop of water is formed from $n$ small drops of water,the energy loss is $3E$,where $E$ is the energy of the bigger drop. The radius of the bigger drop is $R$ and that of the smaller drop is $r$. Then the value of $n$ is:

$8$ mercury drops coalesce to form one mercury drop. The energy changes by a factor of:

Fill in the blanks:
$(i)$ $A$ bubble in water has .......... free surface.
$(ii)$ $A$ bubble in air has .......... free surface.
$(iii)$ $A$ rain drop has .......... free surface.

Vedclass Test Series

Exam Paper Generator

Online Exam Module