Question

If the density of a metal is $8.2 gm/cc.$ Then what is its relative density?
A) $8.2$
B) $\dfrac{{1}}{8.2}$
C) $0.082$
D) $820$

Answer 1

Hint: The relative density of an object is the ratio of the object’s density to the density of water. It is a dimensionless quantity as it is a ratio of two same physical quantities. Relative density is also known as specific gravity.

Complete step by step solution:
We know that the
Density of water $\left( {{\rho _w}} \right) = 1{{gm}/ {cc}}$
And it is given that the
Density of the metal $\left( {{\rho _{metal}}} \right) = 8.2{{gm}/{cc}}$
Now we will take the ratio of metal’s density to the density of water:
$\therefore \dfrac{{{\rho _{metal}}}}{{{\rho _w}}} = \dfrac{{8.2}}{1}$
$ \Rightarrow \dfrac{{{\rho _{metal}}}}{{{\rho _w}}} = 8.2$
Hence, the relative density of metal is found to be 8.2.

The correct option is (A).

Additional information: Relative density is also called specific gravity as it can tell us whether a given substance will float or sink in water. When the specific gravity of an object will be greater than 1, then the mass of the object will be greater than the mass of volume displaced by the object(which according to the Archimedes principle is buoyant force). So the weight of the object will be more than buoyant force. Hence it will sink and when it will be less than 1 for an object, then the weight of the object will be less than the buoyant force. Hence it will float.

Note: Before finding the relative density of an object, Always check the units of the object’s density and use the density of water in the same units for taking the ratio. Relative density also has some practical applications as it is used by geologists to find the mineral content in a rock.