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**Hint:**The Moon has a weaker gravitational force than Earth because it is smaller. In reality, the Moon has only a sixth of the gravity of Earth. This means that on the Moon, you weigh six times less than you do on Earth.

**Complete step by step answer:**

The weight of an object is the gravitational force acting on it, and it can be calculated by multiplying the mass by the acceleration of gravity,

$W=mg$

Here, $W$ is the weight of the object, $m$ is the mass of the object and $g$ is the acceleration due to gravity. Since the weight is a force, its SI unit is the newton (N). It is given that the weight of the object on earth is 20 N and we need to find the weight of the object on the surface of the moon. That is,

\[m = \dfrac{w}{g}\]

Substituting the values to the formula, we get

\[m = \dfrac{{20}}{{10}}\]

That is,

\[m = 2\,kg\]

Now that it has been mounted on the moon, its acceleration due to gravity would be 1/6\[\left( {{g^1}} \right)\] that of the earth. That is,

\[W = m{g^1}\]

\[\Rightarrow W = 2 \times \dfrac{g}{6}\]

\[\Rightarrow W = \dfrac{{10}}{3}\]

\[\therefore W = 3.33,N\]

**Hence, the weight of the object on the moon is 3.33 N.**

**Note:**Remember that the weight of an object is the gravitational force acting on it, and it can be calculated by multiplying the mass by the acceleration of gravity. Keep in mind the equation, $W=mg$.

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