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**Hint:**To solve this question, we need to use the formula for the gravitational force on a body on the surface of the earth. Then we need to substitute the approximate value of the acceleration due to gravity on the surface of the earth. Also, we need to substitute the value of the force given in the question, after which we will get the required value of $Z$.

**Formula used:**The formula used to solve this question is given by

$F = mg$, here $F$ is the magnitude of the gravitational force acting on a body on a particle of mass $m$, and $g$ is the acceleration due to gravity on the surface of earth.

**Complete step-by-step solution:**

We know that the gravitational force acting on a body on the surface of the earth is given by the expression

$F = mg$

Now, we know that the value of the acceleration due to gravity on the surface of the earth is approximately equal to $10m/{s^2}$. The value of the force given in the question is equal to $1N$. Also, the mass of the body is given as $Zkg$. Therefore substituting $F = 1N$ $m = Zkg$ and $g = 10m/{s^2}$ in the above expression, we get

$1 = 10Z$

Dividing both sides by $10$, we get

$Z = \dfrac{1}{{10}}$

$ \Rightarrow Z = 0.1$

Thus, the value of $Z$ is equal to $0.1$.

**Hence, the correct answer is option A.**

**Note:**The unit of force given here is called one kilogram force. It is the non standard, gravitational metric unit of the force. It is a measure of the gravitational force exerted by the earth on an object having a mass equal to one kilogram.

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