A spherical soap bubble of radius $3\,cm$ is formed inside another spherical soap bubble of radius $6\,cm$. If the internal pressure of the smaller bubble of radius $3\,cm$ in the above system is equal to the internal pressure of the another single soap bubble of radius $r\,cm$. The value of $r$ is.......

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......$cm$

Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, then which of the following relation is correct?

The excess of 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

Pressure inside two soap bubbles are $1.02 \,atm$ and $1.05 \,atm$ respectively. The ratio of their surface area is .........

Two spherical soap bubbles formed in vacuum has diameter $3.0\,mm$ and $4.0\,mm$ . They coalesce to form a single spherical bubble. If the temperature remains unchanged, find the diameter of the bubble so formed ....... $mm$