Two soap bubbles of radii $3r$ and $4r$ in contact with each other. The radius of curvature of the interface between bubbles is

There is small hole in a hollow sphere. The water enters in it when it is taken to a depth of $40 \,cm$ under water. The surface tension of water is $0.07 \,N / m$. The diameter of hole is .......... $mm$

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 ....... $mm$

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be $75\, cm$ of $Hg$ and the density of water to be $1/10  $ of the density of mercury, the depth of the lake is ....... $m$

The excess pressure due to surface tension in a spherical liquid drop of radius r is directly proportional to

A $U-$ tube with limbs of diameters $5\, mm$ and $2\, mm$ contains water of surface  tension $7 \times 10^{-2}$ newton per metre, angle of contact is zero and density $10^3\, kg/m^3$. If $g$ is $10 \,m/s^2$, then the difference in level of two limbs is :-