What is the relation between $kgf$ and $N$?
Show the relation as,
(a) $1kgf=\ldots N$
(b) $1N=\ldots kgf$

Hint: The units such as the gram-force and kilogram-force are not perfectly explained units up to the tie when CGPM mentioned a standard constant acceleration of gravity as \[g=9.8m{{s}^{-2}}\]. In 1901, the need for standardising these values became necessary, as they had been used in low-precision measurements of force before this period of time. The \[kgf\] is an abbreviation of kilogram force. This was not a part of the international system of unit, which is abbreviated as SI. This was introduced in 1960. The SI unit of force can be defined as the Newton.

Complete answer:
\[1kgf\] which is the abbreviation for one kilogram force is defined as the force applied by one kilogram mass when it is placed in a gravitational field of magnitude \[9.8m{{s}^{-2}}\].
And force equivalent to this condition will be given as,
\[F=ma\]
That is,
\[\begin{align}
  & F=1kgf=1kg\times 9.8m{{s}^{-2}} \\
 & \Rightarrow 1kgf=9.8N \\
\end{align}\]
Hence the value of one kilogram force in terms of newton has been obtained. Now the value of one newton in terms of kilogram force can be written as,
\[\begin{align}
  & 1kgf=9.8N \\
 & 1N=\dfrac{1}{9.8}kgf \\
\end{align}\]

Note:
One newton is defined as the force required to accelerate one kilogram of mass I the same direction of the exerted force at a rate of one metre per second square, \[\left( 1m{{s}^{-2}} \right)\]. The acceleration can be found by taking the rate of variation of velocity with respect to the time taken. The newton has been considered to be the universally accepted unit for the force. That is it is the unit of force mentioned in the SI unit system. The name has been obtained after the great scientist sir Isaac Newton.