The value of gravity (g) on the Moon is ______ of that on the earth's surface.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1/6
The acceleration due to gravity on the surface of a body is \(g=\frac{GM}{R^2}\): it grows with the body’s mass and falls with the square of its radius. The Moon has about \(\frac{1}{81}\) of the Earth’s mass and about \(\frac{3}{11}\) of its radius.
\(\displaystyle \frac{g_{\text{Moon}}}{g_{\text{Earth}}}=\frac{1}{81}\times\left(\frac{11}{3}\right)^2=\frac{121}{729}\approx\frac{1}{6}\)
So \(g\) on the Moon is about \(1.6\,\mathrm{m/s^2}\) against \(9.8\,\mathrm{m/s^2}\) on the Earth, and a body weighs about one-sixth as much there