Understanding Mass and Weight: Earth vs. Moon

The question asks about the mass of an object on the Moon, given its mass on Earth. This question tests the understanding of the fundamental difference between mass and weight.

What is Mass?

Mass is a measure of the amount of matter in an object. It is an intrinsic property of the object, meaning it does not change depending on where the object is located. Whether the object is on Earth, the Moon, in space, or anywhere else, its mass remains constant unless some matter is added to or removed from it.

What is Weight?

Weight, on the other hand, is the force of gravity acting on an object. It is calculated using the formula: Weight = mass \(\times\) gravitational acceleration (\(\text{W} = \text{m} \times \text{g}\)). Since the gravitational acceleration (\(\text{g}\)) varies depending on the celestial body or location, an object's weight will change from place to place. The Moon has significantly less gravity than Earth (approximately 1/6th of Earth's gravity).

Applying the Concepts to the Question

The question states the object has a mass of 100 kg on Earth. Since mass is a measure of the amount of matter and is constant regardless of location, the object will have the same amount of matter on the Moon as it does on Earth.

Therefore, its mass on the Moon will be the same as its mass on Earth.

Analyzing the Options

• Option 1: 0 kg
  This is incorrect. An object that exists and has matter must have a mass greater than zero.
• Option 2: 100 kg
  This is correct. Mass is constant and does not change with location. If the mass on Earth is 100 kg, the mass on the Moon will also be 100 kg.
• Option 3: 16.7 kg
  This is incorrect. This value is approximately the object's weight on the Moon divided by Earth's standard gravity (\(\approx 100 \text{ kg} \times (1/6) = 16.67 \text{ kg}\), though weight is a force measured in Newtons). It represents a value related to how much lighter the object would feel on the Moon due to lower gravity, but it is not its mass.
• Option 4: 980 kg
  This is incorrect. This value is approximately the object's weight on Earth in Newtons divided by 1 kg (Weight on Earth \(\approx 100 \text{ kg} \times 9.8 \text{ m/s}^2 = 980 \text{ N}\)). It is a measure of force, not mass, and the unit should be Newtons (N). Even as a numerical value, it does not represent the mass on the Moon.

Conclusion

The mass of an object is an intrinsic property that remains constant regardless of the gravitational pull acting on it. Therefore, an object with a mass of 100 kg on Earth will still have a mass of 100 kg on the Moon.

Revision Table: Mass and Weight Concepts

Additional Information: Gravity and Its Effects

The gravitational acceleration on the surface of the Moon is approximately \(\text{1.62 m/s}^2\), whereas on Earth, the average gravitational acceleration is approximately \(\text{9.8 m/s}^2\). This means the Moon's gravity is about 1/6th of Earth's gravity.

While the mass of the 100 kg object remains 100 kg on the Moon, its weight would change:

• Weight on Earth \(\approx 100 \text{ kg} \times 9.8 \text{ m/s}^2 = 980 \text{ N}\)
• Weight on Moon \(\approx 100 \text{ kg} \times 1.62 \text{ m/s}^2 = 162 \text{ N}\)

This difference in weight is why astronauts feel much lighter and can jump higher on the Moon, even though their mass (and the mass of their equipment) hasn't changed.