Question

Mercury has a density of $13.6g/c{m}^3$ . What volume of mercury must be taken to obtain $225g$ of the metal?
(A) $16.54c{m}^3$
(B) $13.86c{m}^3$
(C) $14.54c{m}^3$
(D) $11.86c{m}^3$

Answer 1

Hint: The density of the material is defined as mass per unit volume of the substance. Mathematically, density is defined as the ratio of mass and volume. The $SI$ unit of density is $kg/m^3$ . Relative density is defined as the ratio of density of a substance to the density of the standard substance. Usually water at $4^{\circ }C$ is used as a standard for a liquid or solid and air for a gas. It is a unit less quantity.

Complete step by step answer:
Density: Density is characteristic of property of a substance. It is defined as the ratio of mass of a substance to its volume.
When the volume of an object is fixed, the density is directly proportional to the mass of the object.
 $Density={\displaystyle \frac{mass(inkg)}{Volume(in{m}^3)}}$
So, $SI$ unit of density is ${\displaystyle \frac{kg}{m^3}}$
Given, density of mercury
 $p=13.6g/c{m}^3;$
Mass of mercury, $m=225g;$
Volume of mercury, $v=?$
Now, density, $p={\displaystyle \frac{mass}{volume}}={\displaystyle \frac{m}{v}}$
Or $v={\displaystyle \frac{m}{p}}={\displaystyle \frac{225}{13.6}}=16.54c{m}^3$

So, the correct answer is “Option A”.

Note:
Relative density is defined as the ratio of density of a substance to the density of the standard substance. Usually water at $4^{0}c$ is used as a standard for a liquid or solid and air for a gas. It is a unit less quantity. It is used for determining the density of unknown substances from the known density of another substance. It is used by geologists to kindle the mineral content into the rock. Testing purity of substances like gold. A large body of matter with no definite shape is called mass. Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic meter. Dimension of volume is $L^3$ . Matter is anything that occupies space and has mass. Area is the amount of space occupied by a two-dimensional flat object in a plane. Weight is measurement of an object's heaviness.