Question

$1N = Z kgf$ (approx.), then what is the value of $Z$?
A.$0.1$
B.$1$
C.$10$
D.$0$

Answer 1

Hint: Newton is the SI unit of force. Newton’s Second Law of Motion describes that rate of change in momentum of a moving body is equal to applied force. We will make use of this law and try to find out the value.

Complete Solution step by step:
$F = ma$ (Newton’s Second Law of Motion)
$m = $mass of body
$a = acceleration$
SI Unit of Mass $ = kg$
SI Unit of Acceleration $ = \dfrac{m}{{{s^2}}}$
SI Unit of Force $ = \dfrac{{kg \times m}}{{{s^2}}} = N$
The kilogram-force, is a gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in a $9.80665\dfrac{m}{{{s^2}}}$ gravitational field. That is, it is the weight of a kilogram under standard gravity.
$N$is used as SI unit of force but sometimes in metric standards we use $kgf$ as unit of force.
$1N = 1kg \times 1\dfrac{m}{{{s^2}}}$
$1kgf = 1kg \times 9.807\dfrac{m}{{{s^2}}}$
$1kgf = \left( {1kg \times 1\dfrac{m}{{{s^2}}}} \right) \times 9.807$

$1kgf = 1N \times 9.807$
$1N = \dfrac{1}{{9.807}}kgf$
$1N = 0.1019kgf$
$1N = 0.1kgf$(approx.)
If we compare our over equation with the expression given in the question, we will find that the value of $Z$ in question is $0.1$. So, we can say $1N$ is approximately equal to $0.1kgf$. $kgf$is a bigger unit than $N$ Option A is correct.

Note: $1kgf$ is equal to $9.8N$(approx.). So, we can directly calculate the value of $1N$ in $kgf$. While calculating if we need the exact value then we have to take the exact value of g that is $9.807\dfrac{m}{{{s^2}}}$.