Question

Mass of a man is 60 Kg, his mass on the moon will be :

• A. \(60 \ \text{Kg}\)
• B. \(10 \ \text{Kg}\)
• C. \(98 \ \text{Kg}\)
• D. \(0 \ \text{Kg}\)

Hint:

Key difference: {Mass:} Amount of matter. Constant everywhere. Unit: Kilogram (Kg). {Weight:} Force of gravity on mass (\(W=mg\)). Varies with location (depends on \(g\)). Unit: Newton (N). Your mass is the same on Earth, the Moon, Jupiter, or in deep space. Your weight, however, changes significantly. Don't confuse the two!

Answer 1

The Correct Option is A

Concept: It is crucial to distinguish between mass and weight.
Mass is a measure of the amount of matter in an object. It is an intrinsic property of the object and remains constant regardless of its location. The SI unit of mass is the kilogram (Kg).
Weight is the force of gravity acting on an object. It depends on both the mass of the object and the acceleration due to gravity at its location (\(W = mg\)). The SI unit of weight is the Newton (N). Step 1: Identify the given quantity The mass of the man on Earth is given as \(60 \ \text{Kg}\). Step 2: Understand how mass changes with location Mass is an inherent property of an object, representing the quantity of matter it contains. This quantity of matter does not change whether the man is on Earth, on the Moon, or anywhere else in the universe (unless he gains or loses actual matter, which is not the case here). Step 3: Consider the effect of the Moon's gravity The Moon has a weaker gravitational pull than Earth. The acceleration due to gravity on the Moon is approximately \(1/6\text{th}\) of that on Earth (\(g_{\text{moon}} \approx \frac{1}{6} g_{\text{earth}}\)). This means the man's {weight} on the Moon would be different (approximately \(1/6\text{th}\) of his weight on Earth). If his weight on Earth is \(W_E = 60 \ \text{Kg} \times g_{\text{earth}}\), his weight on the Moon would be \(W_M = 60 \ \text{Kg} \times g_{\text{moon}} = 60 \ \text{Kg} \times \frac{1}{6} g_{\text{earth}} = 10 \ \text{Kg} \times g_{\text{earth}}\). If we were considering "effective mass" based on weight, then 10Kg might seem plausible, but the question explicitly asks for "mass". Step 4: Determine the man's mass on the Moon Since mass is a constant property and does not depend on the gravitational field, the man's mass on the Moon will be the same as his mass on Earth. Therefore, his mass on the Moon will still be \(60 \ \text{Kg}\). Option (2) \(10 \ \text{Kg}\) would be related to his weight on the moon if \(g_{\text{earth}}\) was roughly \(9.8 m/s^2\), then his weight on Earth would be \(60 \times 9.8 \approx 588 N\). His weight on the moon would be \(1/6 \times 588 N \approx 98 N\). If this \(98 N\) weight was divided by Earth's \(g\) (\(9.8 m/s^2\)), you'd get an "equivalent Earth mass" of \(10 Kg\), but this is a misinterpretation of the question. The question asks for mass, not an equivalent mass based on lunar weight compared to Earth's gravity. Option (3) \(98 \ \text{Kg}\) might come from confusing mass with weight in Newtons (e.g., if \(g=9.8\), a \(10 \text{Kg}\) mass has a weight of \(98 \text{N}\)), but mass is in Kg. The correct answer is that his mass remains \(60 \ \text{Kg}\).