Question

Define $1kgf$. How is it related to the SI unit of force?

Answer 1

Hint: Force is defined as the rate of change of momentum with respect to time. The gravitational force exerted by the earth causes an acceleration in all the objects residing on earth and it is known as the Acceleration due to Gravity.

Complete answer:
According to Newton’s second law of motion, Force\[\left( F \right)\] is defined as the rate of change of momentum$\left( p \right)$ with respect to time$\left( t \right)$. Mathematically speaking,
$F = \dfrac{{dp}}{{dt}}$
$ \Rightarrow F = \dfrac{{d\left( {mv} \right)}}{{dt}}$...........$\left[ {\because p = mv} \right]$
$ \Rightarrow F = m\dfrac{{dv}}{{dt}}$
$ \Rightarrow F = ma$...........$\left[ {\because a = \dfrac{{dv}}{{dt}}} \right]$
So, mathematically, force can be defined as the product of mass and acceleration of a body.
According to Newton’s Law of Gravitation, every object in the universe exerts an attractive force on every other object, and that force is known as the Gravitational Force. So, like every other object in the universe, earth also pulls all the objects around it with some gravitational force. That gravitational force causes an acceleration on every object around it. That acceleration is known as the acceleration due to gravity$\left( g \right)$. It can be calculated by,
$g = \dfrac{{GM}}{{{R^2}}}$
Where, $G = $Universal Gravitational Constant $ = 6.67 \times {10^{ - 11}}{m^3}k{g^{ - 1}}{s^{ - 2}}$
$M = $ mass of earth$ = 6 \times {10^{24}}kg$
$R = $ radius of earth$ = 6.4 \times {10^6}m$
Substituting these values in the formula, we get,
$g = 9.8m{s^{ - 2}}$
Now, the force exerted on an object of mass $1kg$ because of the acceleration due to gravity is known as $1kgf$. This force is also known as the weight$\left( W \right)$ of the object. So,
$W = mg$
$ \Rightarrow W = 1kg \times 9.8m{s^{ - 2}}$
$ \Rightarrow W = 9.8N$
$\therefore 1kgf = 9.8N$

Note: The acceleration due to gravity acting on the object does not depend on the mass of the object. Which means that no matter what the mass of the object is, the acceleration action on it would be the same. And that is the reason why any object free falling, falls with the same acceleration and takes the same amount of time to reach ground.