Question

6 litres of kerosene oil is found to weigh 5.28 kg. Find the density of kerosene oil in
(a) CGS system
(b) SI system

Answer 1

Hint
the formula of density is the ratio of mass and its volume i.e. $density = \dfrac{{mass}}{{volume}}$
For the CGS system the mass is in gram and volume in cm3 while in SI unit the mass is in kg and volume is in m3. To convert kilogram into gram, use the relation i.e. $1kg = 1000g$and to convert the litres into cm3, we use the relation i.e. $1litre = 1000c{m^3}$ and to convert litres into m3 use the relation i.e. $1litre = {10^{ - 3}}{m^3}$.

Complete step by step answer
It is given that, Volume of kerosene oil is $V = 6litres$
Weight of kerosene oil is $M = 5.28kg$
We have to find the density of the kerosene oil.
For this we use the formula i.e. $density = \dfrac{{mass}}{{volume}}$ ………………………… (1)
Part (a): In CGS system of unit:
In CGS units the mass must be taken in gram and volume must be taken in cm3
As, in the question mass is given in kg, therefore to convert it into gram we use the relation i.e. $1kg = 1000g$, then mass will become $M = 5.28 \times 1000g = 5280g$
The volume is also given in litres, therefore to convert it into cm3 we have to use the relation i.e. $1litre = 1000c{m^3}$, then volume will become $V = 6 \times 1000c{m^3} = 6000c{m^3}$
Put the values of mass and volume in equation (1), we get
$density = \dfrac{{5280}}{{6000}} = 0.88gc{m^{ - 3}}$
Hence, the density in CGS units is $0.88gc{m^{ - 3}}$
Part (b): In SI system of units:
As in the SI system of units, the mass must be in kg and volume be in cubic meters.
In the question mass is given in kg so no need to convert it then mass is $M = 5.28kg$
And volume is given in litres, therefore to convert it into m3 we use the relation i.e. $1{m^3} = 1000litres$ or we can say $1litre = {10^{ - 3}}{m^3}$ hence the volume will become $V = 6 \times {10^{ - 3}}{m^3}$
Substitute the values in equation (1), we get
$\Rightarrow density = \dfrac{{5.28}}{{6 \times {{10}^{ - 3}}}} = 880kg{m^{ - 3}}$
Hence, the density in the SI unit is $880kg{m^{ - 3}}$.

Note
It must be remembered that, In the CGS system the unit of length, mass and time are centimetre (cm), gram (g) and second (s), respectively. In the SI system the unit of length, mass and time are metre (m), kilogram (kg) and second (s), respectively. The SI system is an extended version of the MKS system or the metric system, where, apart from length, mass and time, there are six more fundamental quantities, viz., temperature (kelvin, K), luminous intensity (candela, cd), electric current (ampere, A), amount of substance (mole, mol), angle (radian, rd) and solid angle (steradian, st-rd).