Excess pressure inside a soap bubble is three times that of the other bubble, then the ratio of their volumes will be

A soap bubble, having radius of $1\; \mathrm{mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}\; N / m$. The pressure inside the bubble equals at a point $Z_{0}$ below the free surface of water in a container. Taking $g=10\; \mathrm{m} / \mathrm{s}^{2}$ density of water $=10^{3} \;\mathrm{kg} / \mathrm{m}^{3},$ the value of $\mathrm{Z}_{0}$ is......$cm$

A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces a certain increase per minute in the volume of the bubble, irrespective of its internal pressure. The graph between the pressure inside the soap bubble and time $t$ will be-

If the radius of a soap bubble is four times that of another, then the ratio of their excess pressures will be

The pressure inside a small air bubble of radius $0.1\, mm$ situated just below the surface of water will be equal to   [Take surface tension of water $70 \times {10^{ - 3}}N{m^{ - 1}}$ and atmospheric pressure = $1.013 \times {10^5}N{m^{ - 2}}$]

Air (density $\rho$ ) is being blown on a soap film (surface tension $T$ ) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$, the speed at which the bubble formed is