Three small identical bubbles of water having the same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is:

$A$ long cylindrical glass vessel has a pinhole of diameter $0.2 \,mm$ at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water,$T=0.07 \,N/m$,acceleration due to gravity,$g=10 \,m/s^2$) (in $\,cm$)

$A$ bubble of $8$ mm diameter is formed in the air. The surface tension of soap solution is $30$ dynes/cm. The excess pressure inside the bubble is ........ $dynes/cm^2$.

$A$ small soap bubble of radius $4 \ cm$ is trapped inside another bubble of radius $6 \ cm$ without any contact. Let $P_2$ be the pressure inside the inner bubble and $P_0$ be the pressure outside the outer bubble. The radius of another bubble with a pressure difference $P_2 - P_0$ between its inside and outside would be....... $cm$.

An air bubble in a water tank rises from the bottom to the top. Which of the following statements are true?

The excess pressure inside a bubble in water is $P_1$. The excess pressure inside a drop of the same radius is $P_2$. Then: