To understand how the weight of an object changes between the Earth and the Moon, we need to differentiate between mass and weight:

1. Mass is constant: The mass of an object remains the same regardless of its location. It is measured in kilograms (kg). In this case, the object has a mass of 10 kg.
2. Weight depends on gravity: Weight is the force exerted on an object due to gravity. It is calculated by multiplying the mass of the object by the gravitational acceleration at that location. The formula for weight is: \(W = m \times g\)
   • \(W\) is the weight in newtons (N).
   • \(m\) is the mass in kilograms (kg).
   • \(g\) is the acceleration due to gravity, measured in meters per second squared (m/s²).
3. Gravitational acceleration comparison:
   • On Earth, \(g \approx 9.8 \, \text{m/s}^2\).
   • On the Moon, \(g \approx 1.6 \, \text{m/s}^2\).
4. Calculate the weight on Earth: \(W_{\text{Earth}} = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N}\)
5. Calculate the weight on the Moon: \(W_{\text{Moon}} = 10 \, \text{kg} \times 1.6 \, \text{m/s}^2 = 16 \, \text{N}\)

Therefore, the object weighs less on the Moon than on Earth because the gravitational acceleration on the Moon is much weaker than on Earth.

Conclusion: The correct answer is: The object weighs less on the Moon than on Earth.