A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $\mathrm{P}_2$. The speed of water flowing out of the pipe is ($\rho=$ density of water)

A completely filled water tank of height ' $h$ ' has a hole at the bottom. The total pressure of the bottom is 4 H and atmospheric pressure is H . The velocity of water flowing out of the hole is ( $\rho=$ density of water)

A metal sphere of radius R, density $\rho_1$ moves with terminal velocity $\mathrm{V}_1$ through a liquid of density $\sigma$. Another sphere of same radius but density $\rho_2$ moves through same liquid. Its terminal velocity is $\mathrm{V}_2$. The ratio $\mathrm{V}_1: \mathrm{V}_2$ is

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1>\rho_2>\rho_3$ ) having same value of surface tension T , rise to the same height in three identical capillaries. Angle of contact $\theta_1, \theta_2$ and $\theta_3$ respectively obey