The energy required to blow a bubble of radius $4 \mathrm{cm}$ and $3 \mathrm{cm}$ in the same liquid is in the ratio of :

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 column of water height H, then the depth of lake is 

A soap film is created in a small wire frame as shown in the figure. The sliding wire of mass $m$ is given a velocity $u$ to the right and assume that $u$ is small enough so that film does not break. Plane of the film is horizontal and surface tension is $T$. Then time to regain the original position of wire is equal to :

A rectangular massless blade (as shown in figure) is placed on a water surface (surface tension $T=\frac{1}{7}\times {10}^{-1} \mathrm{N} {\mathrm{m}}^{-1}$. Perimeter of the middle opening is $4a$. Minimum force needed to lift this blade-up is $\left(a=5 \mathrm{cm}\right)$