If W amount of work is required to form a bub | vedclass

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

Question

(D) The volume of a spherical bubble is given by $V = \frac{4}{3} \pi R^3$,which implies $R = \left( \frac{3V}{4\pi} \right)^{1/3}$.Therefore,$R^2 = \

Vedclass · Accepted Answer

$\sqrt[3]{4} \, W$

Vedclass · Answer

(D) The volume of a spherical bubble is given by $V = \frac{4}{3} \pi R^3$,which implies $R = \left( \frac{3V}{4\pi} ight)^{1/3}$.Therefore,$R^2 = \left( \frac{3}{4\pi} ight)^{2/3} V^{2/3}$,which means $R^2 \propto V^{2/3}$.The work done $W$ to form a soap bubble (which has two surfaces) is $W = T 	imes \Delta A = T 	imes 2(4\pi R^2) = 8\pi R^2 T$.Since $W \propto R^2$ and $R^2 \propto V^{2/3}$,we have $W \propto V^{2/3}$.Thus,$\frac{W_2}{W_1} = \left( \frac{V_2}{V_1} ight)^{2/3} = \left( \frac{2V}{V} ight)^{2/3} = 2^{2/3} = (2^2)^{1/3} = \sqrt[3]{4}$.Therefore,$W_2 = \sqrt[3]{4} \, W$.

If $W$ amount of work is required to form a bubble of volume $V$,then how much work is required to form a bubble of volume $2V$?

Similar Questions

Air is pushed into a soap bubble to increase its radius from $R$ to $2R$. In this case, the pressure inside the bubble

Let $n$ be the number of liquid drops,each with surface energy $E$. These drops join to form a single drop. In this process:

The excess pressure inside an air bubble of radius $r$ just below the surface of water is $p_1$. The excess pressure inside a drop of the same radius just outside the surface is $p_2$. If $T$ is surface tension,then

The excess pressure in a soap bubble is thrice that in another one. Then the ratio of their volume is

Vedclass Test Series

Exam Paper Generator

Online Exam Module