$A$ liquid mixture of volume $V$ has two liquids as its ingredients with densities $\alpha$ and $\beta$. If the density of the mixture is $\sigma$,then the mass of the first liquid in the mixture is ............

The densities of ice and water are $\rho$ and $\sigma$ respectively. What is the change in volume when a mass $M$ of ice melts?

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

$A$ $U$-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are initially in level with $10.0 \; cm$ of water in one arm and $12.5 \; cm$ of spirit in the other. 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 (in $cm$) of mercury in the two arms? (The specific gravity of spirit is $0.8$.)

The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface. The atmospheric pressure is $75 \, cm$ of mercury. The ratio of the density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metres 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 $4^{\circ}C$.