A cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of density of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is $g$, the spring constant of the spring is:

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is ${\rho _i} = 0.917\,g/c{m^3}$.

A body floats in a liquid contained in a beaker. If the whole system as shown in figure falls freely under gravity, then the upthrust on the body due to liquid is

A cubical block of wood of specific gravity $0.5$ and a chunk of concrete of specific gravity $2.5$ are fastened together. The ratio of the mass of wood to the mass of concrete which makes the combination to float with its entire volume submerged under water is

$Assertion :$ A thin stainless steel needle can lay floating on a still water surface.
$Reason :$ Any object floats when the buoyancy force balances the weight of the object

What is buoyancy ?