To calculate the weight of the object on the Moon, we need to consider the difference in gravitational force between the Earth and the Moon. The Moon's gravitational force is about one-sixth of the Earth's gravitational force. So, the weight of the object on the Moon will be:

Weight on Moon = Weight on Earth / 6

Given weight on Earth = 120 N

Weight on Moon = 120 N / 6 = 20 N

Therefore, the object will weigh 20 N on the Moon.