The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth '$h$' of the lake is ($\rho$ = density of water in the lake, $g$ = acceleration due to gravity, $P_0$ = atmospheric pressure).

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

What is the effect of pressure on the boiling point of water?

Three liquids of densities $d, 2d$,and $3d$ are mixed in equal volumes. Then the density of the mixture is

$A$ 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 $Hg = 13.6 \times 10^3 \, kg/m^3$)

Find the depth of a lake at which the density of water is $1\%$ greater than at the surface. Given the compressibility of water $K = 50 \times 10^{-6} \text{ atm}^{-1}$. (Take $1 \text{ atm} = 10^5 \text{ Pa}$) (in $\text{ km}$)