Gauge pressure is defined as:

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

If two liquids of same masses but densities $\rho_1$ and $\rho_2$ respectively are mixed,then the density of the mixture is given by:

Why is it difficult to cook on hills?

$A$ vessel with a square cross-section and a height of $6 \ m$ is vertically partitioned. $A$ small window of $100 \ cm^2$ with a hinged door is fitted at a depth of $3 \ m$ in the partition wall. One part of the vessel is filled completely with water and the other side is filled with a liquid having a density of $1.5 \times 10^3 \ kg/m^3$. What force needs to be applied on the hinged door so that it does not open (in $N$)? (Acceleration due to gravity $= 10 \ m/s^2$)

$A$ uniform long tube is bent into a circle of radius $R$ and it lies in a vertical plane. Two liquids of the same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is