The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. The atmospheric pressure is $75 \, cm$ of mercury. The ratio of the density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metres is:

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,the temperature is constant,and surface tension is neglected,what is the depth of the lake (in $m$)?

An open-ended $U$-tube of uniform cross-sectional area contains water (density $10^3 \ kg \ m^{-3}$). Initially,the water level stands at $0.29 \ m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \ kg \ m^{-3}$ is added to the left arm until its length is $0.1 \ m$,as shown in the schematic figure. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass $M$ of ice melts?

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.

Define pressure. Give the $SI$ and $CGS$ unit of pressure.