$A$ bubble from the bottom of a lake rises to its surface. Its volume doubles in the process. Assuming isothermal conditions, atmospheric pressure $= 75 \, cm$ of $Hg$, and the ratio of the densities of mercury and water $= 40/3$. The depth of the lake will be ..... $m$.

If a vessel containing a fluid of density $\rho$ up to height $h$ is accelerated vertically downwards with acceleration $a_0$,then the pressure by the fluid at the bottom of the vessel is given by the equation ........ ($p_0$ denotes the atmospheric pressure and $g$ denotes the acceleration due to gravity).

Find the depth of a lake at which the density of water is $1\%$ greater than at the surface. Given the compressibility of water $K = 50 \times 10^{-6} \text{ atm}^{-1}$. (Take $1 \text{ atm} = 10^5 \text{ Pa}$) (in $\text{ km}$)

The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth '$h$' of the lake is ($\rho$ = density of water in the lake, $g$ = acceleration due to gravity, $P_0$ = atmospheric pressure).

$A$ tank $5 \ m$ high is half-filled with water and then is filled to the top with oil of density $0.85 \ g/cm^3$. The pressure at the bottom of the tank,due to these liquids is ....... $g \ dyne/cm^2$.

$A$ 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