If the radius of the opening of the dropper is $$r$$, the vertical force due to the surface tension on the drop of radius R (assuming $$r$$ << R) is

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

STATEMENT - 1 :

The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT - 2 :

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it