Question

Density of wood is 0.5 g/c.c in the C.G.S system of units. The corresponding value in M.K.S units is?

Answer 1

The CGS system stands for the centimeter-gram-second system of units. It is the unit system where length is measured in cm, mass in gram and time in seconds as standard. To convert from one metric system to another we either multiply or divide the number in multiples of 10.

Formula used:

To convert from CGS to MKS

$1 cm= {10^{-2}}m$

$1 {cm^3}= {10^{-6}} {m^3}$

$1 gm= {10^{-3}}kg$

Complete solution:

The density of a material (here wood) is the ratio of mass and volume of a substance. The mass of a substance is measured in units of gm, kg, etc, while the volume is measured as the cube of cm, m, etc.

We have,

Density=$\dfrac{mass}{volume}$

Considering mass as m and let the length of side be l

$\therefore density=\dfrac{m}{{{l}^{3}}}$

Unit of density = unit of mass/ unit of cube of l

In CGS system of units,

Unit of density = $\dfrac{gm}{{{(cm)}^{3}}}$

Now, given that the mass of the wood in the CGS system is 0.5 gm/cc, we are asked to convert the CGS value to the MKS value. We can calculate the MKS value by using the unit conversion method.

$\therefore$ In MKS units, it is expressed as

Unit of density = $\dfrac {gm}{cc}=\dfrac {gm}{cm^3}$

We know that,

$1 cm= {10^{-2}}m$

$1 {cm^3}= {10^{-6}} {m^3}$

$1 gm= {10^{-3}}kg$

$\therefore$ The MKS unit of density =$\dfrac {{10^3} kg}{{10^{-6}} {m^3}}$

$\Rightarrow$ Unit of density = ${{10}^{3}}kg/{{m}^{3}}$

Thus, 1 gm/cc is expressed as ${{10}^{3}}kg/{{m}^{3}}$ . Now, let us convert 0.5 gm/cc into MKS units using the above conversion formula.

$\Rightarrow 0.5 \dfrac {gm}{cc}= 0.5\times {10^3} \dfrac {kg}{m^3}$

$\Rightarrow 0.5 \dfrac {gm}{cc}= 500 \dfrac {kg}{m^3}$

Therefore, the density of wood is $500 kg/ {m^3}$ in the MKS system of units.

Additional information:

There are different types of systems of measurement available to us. The S.I system, CGS system, MKS system, Imperial system are some of them. Among these, the S.I system is taken as the standard system of units for measurement. Apart from these, there is the existence of the natural system of units which is defined in terms of the universal physical constants.

Note: The conversion from the CGS system to the MKS system or vice versa is possible by the multiplication or the division of a multiple of 10 to convert from one form to another. In the above problem, we do the same to convert density from gm/cc to kg/${{m}^{3}}$ , which is the unit of measurement of density in the MKS system