$A$ 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 $cm$.

The pressure at the bottom of a water tank is $4 P$,where $P$ is atmospheric pressure. If water is drawn out until the water level decreases by $\frac{3}{5}$ of its initial height,then the pressure at the bottom of the tank is .........

What would be the absolute pressure at a depth of $1 \,km$ below the ocean surface? [Given: density of water $\rho = 10^{3} \,kg/m^{3}$,$g = 10 \,m/s^{2}$,$1 \,atm = 1.01 \times 10^{5} \,N/m^{2}$]

$A$ barometer kept in an elevator reads $76 \, cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cm$ of $Hg$) is ........

$A$ submarine experiences a pressure of $5.05 \times 10^6 \, Pa$ at a depth of $d_1$ in a sea. When it goes further to a depth of $d_2,$ it experiences a pressure of $8.08 \times 10^6 \, Pa.$ Then $d_2 - d_1$ is approximately ........ $m$ (density of water $= 10^3 \, kg/m^3$ and acceleration due to gravity $= 10 \, m/s^2$).

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