Depth of a river is $100 \ m$. Magnitude of compressibility of the water is $0.5 \times 10^{-9} \ N^{-1} \ m^2$. The fractional compression in water at the bottom of the river is (Acceleration due to gravity $= 10 \ m/s^2$)

$A$ liquid $X$ of density $3.36 \, g/cm^3$ is poured into a $U$-tube containing $Hg$ up to a height of $10 \, cm$. Another liquid $Y$ is poured into the left arm to a height of $8 \, cm$. The upper levels of $X$ and $Y$ are at the same height. Find the density of liquid $Y$ in $g/cm^3$. (Density of $Hg = 13.6 \times 10^3 \, kg/m^3$)

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 identical vessels are filled with equal masses of three different liquids $A, B$ and $C$ $(\rho_A > \rho_B > \rho_C)$. The pressure at the base will be

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

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