The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is $n$ times the volume of the second,where $n$ is:

When a large bubble rises from the bottom of a lake to the surface,its radius doubles. If atmospheric pressure is equal to that of a column of water of height $H$,then the depth of the lake is:

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 $2V$?

The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble must be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is $(\varepsilon_0 = \text{permittivity of the free space})$

$A$ bubble has surface tension $S$. The ideal gas inside the bubble has a ratio of specific heats $\gamma = \frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$,the radius of the bubble is $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{a2}$,the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$,respectively.
Which of the following statement$(s)$ is(are) correct?
$(A)$ If the surface of the bubble is a perfect heat insulator,then $\left(\frac{r_1}{r_2}\right)^5 = \frac{P_{a2} + \frac{4S}{r_2}}{P_{a1} + \frac{4S}{r_1}}$
$(B)$ If the surface of the bubble is a perfect heat insulator,then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure.
$(C)$ If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible,then $\left(\frac{r_1}{r_2}\right)^3 = \frac{P_{a2} + \frac{4S}{r_2}}{P_{a1} + \frac{4S}{r_1}}$
$(D)$ If the surface of the bubble is a perfect heat insulator,then $\left(\frac{T_2}{T_1}\right)^{\frac{5}{2}} = \frac{P_{a2} + \frac{4S}{r_2}}{P_{a1} + \frac{4S}{r_1}}$

In Jager's method,at the time of bursting of the bubble,