If the weight of an object on the Earth's surface is 2.5 x 10\(^3\)N, what is its weight on the moon's surface if the gravitational force of the moon is one...

Answer Details

Weight is the force of gravity on a body, \(W = mg\). The mass is a fixed property of the body and does not change when the body is moved to the moon; only \(g\) changes. Since the moon's gravitational field strength is one-sixth of the earth's, the weight there must also be one-sixth of the weight on earth.

Working through the two steps explicitly, first find the mass on earth:

\[m = \frac{W_{e}}{g_{e}} = \frac{2.5\times10^{3}\,\mathrm{N}}{10\,\mathrm{m\,s^{-2}}} = 250\,\mathrm{kg}.\]

The moon's gravitational field strength is

\[g_{m} = \frac{1}{6}\times 10 = 1.667\,\mathrm{m\,s^{-2}},\]

so the weight on the moon is

\[W_{m} = m g_{m} = 250 \times 1.667 = 416.67\,\mathrm{N}.\]

The same result comes directly from \(W_{m} = \tfrac{1}{6}W_{e} = 2500/6 = 416.67\,\mathrm{N}\), which is the quicker route once you have noticed that mass cancels.

The misconception this question targets is the belief that mass itself becomes smaller on the moon. It does not: a \(250\,\mathrm{kg}\) body remains \(250\,\mathrm{kg}\) anywhere, and a beam balance comparing masses would read the same on the moon, while a spring balance measuring force would read one-sixth as much. In the examination, write down which quantity is being asked for, mass in kilograms or weight in newtons, before you start dividing by six.