Question

Why will a block of iron float in mercury but sink in water.

Answer 1

Buoyant force is directly proportional to the density of the fluid in which an object is immersed. Buoyancy is the tendency to rise or float in a fluid. The upward force exerted on objects submerged in fluids is called “Buoyant force”. Mercury is denser than that of iron, hence the solid will float in the mercury though it is a heavier material.

Complete step by step answer:
We know that, the formula for buoyant force is,
$F = \rho Vg = ma$
Where,
$\rho =$ Density of the liquid
V= Volume
m= Mass of the displaced fluid
Therefore, denser the fluid is, greater the buoyancy and buoyant force.
If the density of solid is less than that of the liquid then it will float, if the density of solid is greater than that of liquid then it will sink.
The density of iron, mercury and water is given by,
${\rho _{iron}} = 7874\dfrac{{kg}}{{{m^3}}}$
${\rho _{mercury}} = 13690\dfrac{{kg}}{{{m^3}}}$
${\rho _{water}} = 1000\dfrac{{kg}}{{{m^3}}}$
Clearly, ${\rho _{iron}} \ll {\rho _{mercury}}$ and ${\rho _{iron}} \gg {\rho _{water}}$.
Hence, the block of iron floats in mercury because the density of mercury is more than water.

Thus, a large buoyancy force acts on the block of iron and it floats.

Note: One should always remember that just because something weighs more it doesn’t mean it will sink down the fluid. Every material in nature has different densities and depending on the density whether the object will float or sink will be decided.