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:

Which of the following quantities is expressed as force per unit area?

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?

Explain the hydrostatic paradox.

The limbs of a $U$-tube are lowered into vessels $A$ and $B$,where vessel $A$ contains water. Some air is pumped out through the top of the tube at $C$. The liquids in the left limb (in vessel $A$) and the right limb (in vessel $B$) rise to heights of $10\, cm$ and $12\, cm$ respectively above the free surfaces of the liquids in the vessels. The density of liquid $B$ is ........ $g/cm^3$.

Why is the dam of a water reservoir thick at the bottom?