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:

$A$ 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 ........ $g/cm^2$.

Explain why it is easier to cut an apple with a sharp knife than with a blunt knife.

The pressure of confined air is $p$. If the atmospheric pressure is $P$,then

What is thrust?

$A$ vessel with a square cross-section and a height of $6 \ m$ is vertically partitioned. $A$ small window of $100 \ cm^2$ with a hinged door is fitted at a depth of $3 \ m$ in the partition wall. One part of the vessel is filled completely with water and the other side is filled with a liquid having a density of $1.5 \times 10^3 \ kg/m^3$. What force needs to be applied on the hinged door so that it does not open (in $N$)? (Acceleration due to gravity $= 10 \ m/s^2$)