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 $m$)?

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

Two communicating vessels contain mercury. The diameter of one vessel is $n$ times larger than the diameter of the other. $A$ column of water of height $h$ is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s =$ relative density of mercury and $\rho =$ density of water) by

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \text{ g/cm}^3$) standing initially $20 \text{ cm}$ from the bottom in each arm. An immiscible liquid of density $4.0 \text{ g/cm}^3$ is added to one arm until a layer $5 \text{ cm}$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

In making an alloy,a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$. Then,the specific gravity of the alloy is:

$A$ liquid of mass $1 \ kg$ is filled in a flask as shown in the figure. The force exerted by the flask on the liquid is $(g = 10 \ m/s^2)$ [Neglect atmospheric pressure]: