Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_A, \rho_B$ and $\rho_C$ (where $\rho_A > \rho_B > \rho_C$). The pressure at the bottom of the vessels is:

If a substance of mass $m_1$ and specific gravity $s_1$ is mixed with a substance of mass $m_2$ and specific gravity $s_2$,what is the specific gravity of the mixture?

At shallow depth $h$,the pressure in the ocean is simply given by $P = P_0 + \rho gh$,in which $\rho$ is the density of water and $P_0$ is the air pressure. As we go deeper,the high pressure causes the water to compress and become denser. Which of the following sketches illustrates the correct dependence of the pressure on the depth $h$ ?

Two liquids of densities $\rho_{1}$ and $\rho_{2}$ (where $\rho_{2} = 2\rho_{1}$) are filled behind a vertical wall of height $10 \; m$ and width $w$,as shown in the figure. Each liquid has a height of $h = 5 \; m$. The ratio of the force exerted by the upper liquid on the part $MN$ to the force exerted by the lower liquid on the part $NO$ is (Assume that the liquids do not mix):

Mountaineers suffer from nose bleeding (epistaxis) at higher altitudes. Explain.

$A$ siphon in use is demonstrated in the following figure. The density of the liquid flowing in the siphon is $1.5 \text{ g/cm}^3$. The pressure difference between the points $P$ and $S$ will be