Question

The density of mercury is $5427kg{{m}^{-3}}$ . If the density of water is $1.0\ gm{{L}^{-1}}$ , will mercury float or sink in water?

Answer 1

In order to compare the densities of water and mercury, we need to convert the given values in same units i.e., either we need to convert the unit of density of mercury from $kg{{m}^{-3}}$ to $gm{{L}^{-1}}$ or we need to convert the unit of density of water from $gm{{L}^{-1}}$ to $kg{{m}^{-3}}$ in order to predict that whether mercury will sink or float in water.

Complete answer:
Density is a measure of how closely the molecules of a material are packed together. It can be defined as the mass per unit volume and it is denoted by the symbol D or $\rho$ . Basically, density of a substance is a ratio of its mass to its volume and mathematically, it can be expressed as follows:
$\rho =\dfrac{M}{V}$
Where, $\rho$ represents density, M represents the mass and V represents the volume. Now, if we compare the values of density an object with water, we can predict whether an object is going to sink or float in water as per following rules:
1. If an object has comparatively less density than water, it will tend to float in it.
2. If an object has a comparatively higher density than that of water, then it will tend to sink in it.
These rules can be explained on the basis of Archimedes principle which states that when an object is in water, there are two forces that are acting on that object which are as follows:
a. Gravity which pulls objects downward.
b. Buoyant force which pushes objects upward.
Density plays a crucial role in Archimedes’ principle for determining whether an object will float or sink in water. If the average density of an object is less than water, it will float because the water, having higher density, contains more mass and thus, more weight in the same volume. The buoyant force, which is equal to the weight of the water displaced, is thus greater than the weight of the object and hence, the object will float. Likewise, if an object is denser than water it will sink.
The density of water is $1.0\ gm{{L}^{-1}}$ . In units of $kg{{m}^{-3}}$ , the density of water can be expressed as $1000kg{{m}^{-3}}\ \ \ \ \ \ \left[ \because 1gm{{L}^{-1}}=1000kg{{m}^{-3}} \right]$ . The density of mercury is $5427kg{{m}^{-3}}$ which is more than the density of water. Thus, we can conclude that mercury will sink in water.

Note:
It is important to note that we can also determine whether an object will float or sink in water by two factors i.e., mass and volume. As the mass increases, the object is more likely to sink and as the volume increases, the object is more likely to float.