A streamline flow of a liquid of density ' $\rho$ ' is passing through a horizontal pipe of crosssectional area $A_1$ and $A_2$ at two ends. If the pressure of liquid is ' P ' at a point where flow speed is ' $v$ ', then pressure at another point where the flow of speed becomes 3 v is

The pressure inside a soap bubble A is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of volume of $A$ to that of $B$ is

Glycerine of density $1.25 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ is flowing in conical shaped horizontal pipe. Crosssectional area of the pipe at its both ends is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ respectively. Pressure difference at both the ends is $3 \mathrm{~N} / \mathrm{m}^2$. Rate of flow of liquid in the pipe is

Two spherical soap bubbles of radii '$$a$$' and '$$b$$' in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to