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:

Gauge pressure is defined as:

It is difficult to heal a wound on a mountain. Why? Explain.

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 $\text{ km}$)

In the arrangement shown, both the vessels $A$ and $B$ are identical, but the amount of water in $B$ is double that in $A$. The vessels are closed by identical leak-proof pistons at the same height. The pistons are connected to the ends of a lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now, the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube?

$Assertion$ : Specific gravity of a fluid is a dimensionless quantity.
$Reason$ : It is the ratio of density of fluid to the density of water at $4^{\circ}C$.