$A$ hollow sphere has an inner volume equal to half of its outer volume. If $4/5$ of its volume is submerged when placed in water,what is the density of the material of the sphere? (Density of water = $10^3 \ kg/m^3$)

$A$ cubical block of wood with a side length of $10 \ cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \ cm$ below the interface. The density of oil is $0.6 \ g/cm^3$. The mass of the block is ......... $gm$.

Why do bubbles rise in a soda water bottle?

The loss in weight of a solid when immersed in a liquid at $0^o C$ is $W_0$ and at $t^o C$ is $W$. If the cubical coefficients of expansion of the solid and the liquid are $\gamma_s$ and $\gamma_l$ respectively,then $W$ is equal to:

$A$ hollow sphere of mass $M$ and radius $R$ is immersed in a tank of water (density $\rho_w$). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which make an angle of $45^{\circ}$ with the horizontal as shown in the figure. The tension $T_1$ in each wire is:

$A$ leak-proof cylinder of length $1 \; m,$ made of a metal which has a very low coefficient of expansion,is floating vertically in water at $0^{\circ} C$ such that its height above the water surface is $20 \; cm.$ When the temperature of water is increased to $4^{\circ} C,$ the height of the cylinder above the water surface becomes $21 \; cm.$ The density of water at $T=4^{\circ} C,$ relative to the density at $T=0^{\circ} C,$ is close to