The density of the atmosphere at sea level is $1.29 \; kg/m^3$. Assume that it does not change with altitude. Then how high (in $km$) would the atmosphere extend?

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):

$A$ force of $F = 10 \ N$ is exerted on a surface of area $A = 0.1 \ m^{2}$ at an angle of $60^{\circ}$ with the surface. Find the pressure produced on this surface.

$A$ cubical block of wood, of length $10 \,cm$, floats at the interface between oil of density $800 \,kg/m^3$ and water. The lower surface of the block is $1.5 \,cm$ below the interface. If the depth of water is $10 \,cm$ below the interface and oil is up to $10 \,cm$ above the interface, then the difference in pressure at the lower and the upper face of the wooden block is:
(Assume density of water, $\rho_w = 1000 \,kg/m^3$ and acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,Pa$)

At every point of a liquid at rest,the tangential stress is zero. Explain with reason.

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 $h$ ?