Question

Density of wood is $0.5g/cc$ in the CGS system of units. The corresponding value in MKS units is

Answer 1

Hint: Density is a measure of mass contained in a given volume. The CGS unit of mass is grams and volume is the cubed dimension of length that is Centimeters. To convert the given value into the MKS units we need to know the relation between both of the quantities in different systems of units.

Complete step by step solution:
We know that density is defined as the mass of a body divided by its volume, it can also represent mass per unit volume. It is given by the formula,
$\rho = \dfrac{M}{V}$
where $M$ is the mass of the object and $V$is the volume of the given object.
For mass, we know that the CGS unit of mass is Grams whereas the MKS unit of mass is kilograms. The relationship between both quantities can be given by-
$1kg = 1000g$or
$1g = 0.001kg$
where $g$is the acronym of a gram and $\;kg$ is the acronym for kilogram.
Similarly,
For volume, we know that volume of a material is not a basic unit but is derived from the units of length. It is the measure of total space occupied by it. It contains the $X$,$Y$, and $Z$components of the length of an object thus, the unit of volume should be length cubed or,
$V = {l^3}$
where $V$represents the volume while $l$ is the length of the object.
In the CGS unit system, the unit of length is centimetres while the unit of length in the MKS system of units meters.
The relationship between meters and centimetres is given by-
$1m = 100cm$ or
$1cm = 0.01m$
But this relationship changes as the units are cubed,
$1c{m^3} = {\left( {0.01m} \right)^3}$
$ \Rightarrow 1c{m^3} = 0.000001{m^3}$
or $1c{m^3} = {10^{ - 6}}{m^3}$
It is given in the question that,
The density of the wood in the CGS system of units is-
$\rho = 0.5\dfrac{g}{{cc}}$
Converting this into MKS by the obtained relations,
$\rho = 0.5\dfrac{{{{10}^{ - 3}}kg}}{{{{10}^{ - 6}}{m^3}}}$
$ \Rightarrow \rho = 0.5\dfrac{{{{10}^3}kg}}{{{m^3}}}$
Simplifying this we get,
$\rho = 500kg/{m^3}$

Note: The MKS system, combined with four more primary units of the system, is used all over the world to scientifically represent the quantities. It is known as the SI system of units or the metric unit. Here, apart from seconds (the unit of time), all other quantities have their smaller units as powers of ten.