If a body weighs 12 N on the surface of the earth, how much will it weigh on the surface of the moon where acceleration due to gravity is only one-sixth of that on the earth's surface?

Introduction / Context:
Weight is the force with which a body is attracted towards the centre of a planet due to gravity. It depends on both the mass of the object and the local acceleration due to gravity. This question asks you to compare the weight of the same body on the earth and on the moon, given that gravity on the moon is one-sixth of that on the earth. It illustrates how weight changes from place to place even though mass remains constant.

Given Data / Assumptions:
- Weight on earth, W_earth = 12 N.
- Acceleration due to gravity on the moon, g_moon, is one-sixth of acceleration due to gravity on earth, g_earth.
- We assume mass of the body remains the same on both bodies.

Concept / Approach:
Weight is given by W = m * g, where m is mass and g is local acceleration due to gravity. On the earth, W_earth = m * g_earth. On the moon, W_moon = m * g_moon. Given that g_moon = g_earth / 6, we get W_moon = m * (g_earth / 6) = W_earth / 6. So the weight on the moon is one-sixth of the weight on earth. We simply divide the earth weight by 6 to find the moon weight.

Step-by-Step Solution:
Step 1: Write the expression for weight on earth: W_earth = m * g_earth = 12 N. Step 2: Use the given relation g_moon = g_earth / 6. Step 3: Write weight on the moon: W_moon = m * g_moon. Step 4: Substitute g_moon into this: W_moon = m * (g_earth / 6) = (m * g_earth) / 6. Step 5: Recognise that m * g_earth is W_earth, so W_moon = W_earth / 6 = 12 / 6 = 2 N. Step 6: Therefore, the body weighs 2 N on the moon.

Verification / Alternative check:
You can reason qualitatively: since the moon's gravity is one-sixth of the earth's, any object will feel six times lighter there. A common textbook example is that a person weighing 60 kg force on earth would weigh about 10 kg force on the moon. This proportional reduction matches the calculation done here and supports the conclusion that 12 N on earth becomes 2 N on the moon.

Why Other Options Are Wrong:
12 N: This would imply that weight does not change with gravity, which is incorrect because weight depends directly on local gravitational acceleration.
10 N: This would correspond to a small reduction in weight not justified by the one-sixth gravity factor given in the question.
6 N: This represents one-half of the earth weight rather than one-sixth and is not consistent with the data provided.

Common Pitfalls:
Students sometimes confuse mass and weight, thinking that both remain constant everywhere. Mass is invariant, but weight changes with gravitational field strength. Another mistake is to miss the fraction correctly and multiply instead of dividing by six. Carefully applying W_moon = W_earth * (g_moon / g_earth) prevents such errors. Always pay attention to relative gravity values when moving between different celestial bodies.

Final Answer:
On the surface of the moon the body will weigh 2 N.