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

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 $m$)?

Two stretched membranes of area $2\, cm^2$ and $3\, cm^2$ are placed in a liquid at the same depth. The ratio of pressures on them is

Two substances of densities ${\rho _1}$ and ${\rho _2}$ are mixed in equal volumes and the relative density of the mixture is $4$. When they are mixed in equal masses,the relative density of the mixture is $3$. The values of ${\rho _1}$ and ${\rho _2}$ are

In a $U$-tube as shown in the figure,water and oil are in the left and right sides of the tube,respectively. The heights from the bottom for the water and oil columns are $15 \; cm$ and $20 \; cm$,respectively. The density of the oil is ...... $kg/m^3$. [Take $\rho_{\text{water}} = 1000 \; kg/m^3$]

Pressure at the bottom of a tank of water is $3P$,where $P$ is atmospheric pressure. If water is drawn out till the level of water is lowered by one-fifth,then the pressure at the bottom of the tank is