Question

The density of a material is $ 8{\text{ }}g.c{c^{ - 1}} $ . In a unit system in which the unit length is $ 5cm $ and unit mass is $ 20g $ . What is the density of the material?
(A) 0.02
(B) 50
(C) 40
(D) 12.5

Answer 1

Hint: A substance's density is one of its distinguishing characteristics. The density of a substance is determined by the mass, size, and arrangement of atoms. Density equals the mass of the substance divided by its volume; $ D = \dfrac{m}{v} $ . The densities of objects with the same volume but different mass vary.

Complete Step By Step Answer:
Given that-
Density of a material, $ \rho = 8\dfrac{g}{{cc}} = \dfrac{{8gm}}{{c{m^3}}} $
Now, as per the question:
Unit mass is, $ m = 20g $
And, the unit length (volume in a unit system), $ v = {(5cm)^3} = 125c{m^3} $
So, as we all know the formula of density in a unit system in terms of its mass and volume:-
 $
  \therefore Density = \dfrac{{Mass}}{{Volume}} \\
   \Rightarrow {\rho _{new}} = \dfrac{{20gm}}{{125c{m^3}}} \\
  $
Therefore, the density of a material is the given density upon the new density in a unit system:
 $ \therefore \dfrac{\rho }{{{\rho _{new}}}} = \dfrac{8}{{\dfrac{{20}}{{125}}}} = \dfrac{{125 \times 8}}{{20}} = 50 units $
So, the required density of the given material is $ 50units $ .
Hence, the correct option is (B) 50 .

Note:
The density of a pure substance is equal to its mass concentration in numerical terms. Varied materials have different densities, which can affect things like buoyancy, purity, and packaging. At ordinary temperature and pressure, osmium and iridium are the densest known elements.