Question

Express the units of the force constant of a spring in SI fundamental units.

Answer 1

Hint: The system of units is different for different countries and some of the different systems of units are the CGS system of units, the FPS system of units, the MKS system of units and the SI system of units. The SI system of units is internationally accepted and MKS is a system of units. In the SI unit system there are seven SI base units and three supplementary units.

Complete step-by-step solution:
Hooke’s law states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance. Mathematically Hooke’s law states that applied force equals a constant times the displacement or change of length.
 From Hooke’s law force is given as:
$F=KX$ $\cdots \cdots (1)$
Where $F$ = Force
             $X$ = Displacement
             $K$ = Force constant
The force which causes a change in velocity and change in velocity creates a force. The SI unit of force is newton.
 Displacement is defined as the process in which objects' positions are changed and in displacement the initial position of objects are changed. Displacement is also defined as change in initial position of objects to the final position and displacement is measured in terms of meters.
 Force constant is also called as spring constant
On rearranging the equation (1)
$K={\displaystyle \frac{F}{X}}$
SI unit of spring constant is obtained by replacing force into its unit and also displacement into its unit.
$K={\displaystyle \frac{N}{m}}$
So the SI unit of spring constant is $N{m}^{-1}$ .

Note: Students the supplementary SI units are radian, steradian and Becquerel and base SI units are meter, kilogram, second, kelvin, ampere, candela and mole. All other SI units are derived from these base units and the system of measurement is a collection of units of measurement. Each unit will have a universally recognized size.