An object weighs 18 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?
3 N
Weight is the gravitational force acting on a body and is given by \(W = mg\), so for a fixed mass it depends only on the acceleration due to gravity at the place of measurement.
The mass of the object is an intrinsic property and stays exactly the same everywhere; only the value of \(g\) changes as we move from the Earth to the Moon.
We can first find the mass on Earth, taking \(g_{earth} \approx 10\,\text{m/s}^2\): \(m = \frac{W}{g} = \frac{18}{10} = 1.8\,\text{kg}\).
The acceleration due to gravity on the Moon's surface is about one-sixth of that on Earth's surface, because the Moon has far less mass and a smaller radius, giving \(g_{moon} = \frac{1}{6} g_{earth}\).
Therefore the weight on the Moon is one-sixth of the weight on Earth: \(W_{moon} = \frac{1}{6} \times W_{earth} = \frac{1}{6} \times 18\).
Computing this gives \(W_{moon} = \frac{18}{6} = 3\,\text{N}\), which can be cross-checked as \(m \times g_{moon} = 1.8 \times \frac{10}{6} = 3\,\text{N}\).
The key idea is that weight scales in direct proportion to \(g\) while mass is invariant, so the object weighs 3 N on the surface of the Moon.
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