Question

Define one kilogram, the S.I. unit of mass. How is it related to (i) quintal (ii) metric tonne and (iii) gram?

Answer 1

Hint: The kilogram is the base unit of mass or the SI unit of mass. The SI unit is the abbreviated form of the International System of Units and is a worldwide accepted standard unit of measurement. The kilogram is sometimes written as kilogramme or simply kilo and is denoted by the symbol \[kg\] .

Step by Step Solution
As discussed above, the International System of Units is a worldwide accepted standard and hence any units defined in it should have certain standard measurements that can be checked and set anywhere in the world. The kilogram, a part of the SI units, has also a standard measuring. It is the mass of one thousand cubic centimetres of water that is, if you take a cube of dimensions one centimetre each and fill it with water, the mass contained in it would be equal to one kilogram.
Now, in our daily use, we sometimes measure quantities having much less and much more mass than one kilogram. To use kilogram for all mass measurements would be less wise. Hence any standard unit of measurement should accommodate for such situations. Quintal and metric tonne are the large units of mass whereas gram is a smaller unit of mass. Gram is also the base unit of mass in the CGS unit of measurement.
The relation of kilogram with the other units of mass given to us can be defined as follows
 quintal \[=100kg\] and metric tonne \[=1000kg\]
Although not asked, the relation between a quintal and a metric tonne can be given as
 metric tonne \[=10\] quintal
The relation between a kilogram and a gram can be given as follows
\[1kg=1000grams\]

We have hence successfully defined the kilogram and established its relationship with the other given units of mass.

Note
Any unit of mass would be useless without defining a proper relation of it with other units of the same physical quantity. This is because the quantity does not vary with a variation in the unit of measurement. So the mass of a body should be the same, independent of the fact that it is measured in the SI system or the CGS system or any possible system. A factor for interconversion ensures uniformity and constancy in the physical quantity.