The gauge pressure at a depth of $50 \,m$ in a sea is (Density of sea water is $1025 \,kg \,m^{-3}$ and $g=10 \,ms^{-2}$ ). (in $\,Pa$)

Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h$ $(h < H)$ on one side. Let the density of water be $\rho_w$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h/2$ and wall length $L/2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is

The pressure at half the depth of a lake is $2/3$ of the pressure at its bottom. What is the depth of the lake in $m$?

$A$ barometer tube reads $75 \,cm$ of $Hg$. If the tube is gradually inclined at an angle of $30^{\circ}$ with the horizontal,keeping the open end in the mercury container,then find the length of the mercury column in the barometer tube in $cm$.

What does it mean when the height of a barometer is rising?

The density of the liquid filled in the container is $900 \ kg/m^{3}$. Calculate the force exerted on the bottom of the container. (Given: $g = 10 \ m/s^{2}$) (in $N$)