$A$ 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 ..... $m$.

Why are railway tracks laid on large-sized wooden sleepers?

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

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 ........ $g/cm^3$.

Three liquids of equal masses are taken in three identical cubical vessels $A, B$ and $C$. Their densities are $\rho_{A}, \rho_{B}$ and $\rho_{C}$. The force exerted by the liquid on the base of the cubical vessel is

In the previous problem,if $15.0 \; cm$ of water and spirit each are further poured into the respective arms of the tube,what is the difference in the levels of mercury in the two arms (in $; cm$)? (Specific gravity of mercury $= 13.6$)