Three different liquids are filled in a $U$-tube as shown in the figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ respectively. From the figure, we may conclude that:

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 $m$)?

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

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

$A$ cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$) and its neck is filled with immiscible oil (density $\rho_0$). Then,the pressure at

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 $= 10 \ m/s^2$)