Final answer:
The largest mass of gold for a weight of 1 newton would be on the Moon due to its lower acceleration due to gravity (1.625 m/s²) compared to Earth (9.8 m/s²) and Jupiter (24.5 m/s²).
Step-by-step explanation:
If you had a chunk of gold that weighed 1 newton, the mass of the gold would be greatest on the moon. This is because the acceleration due to gravity is least on the moon, resulting in a greater mass for the same force of weight. On Earth, the acceleration due to gravity is 9.8 m/s², on the Moon it is about 1.625 m/s², and on Jupiter, it is about 24.5 m/s².
Since weight (W) is calculated by the formula W = mass (m) × acceleration due to gravity (g), and we have a constant weight of 1 N, we need to determine the mass by rearranging the formula to m = W/g.
On Earth: m = 1 N / 9.8 m/s²
= 0.102 kg
On the Moon: m = 1 N / 1.625 m/s²
= 0.615 kg
On Jupiter: m = 1 N / 24.5 m/s²
= 0.0408 kg
Therefore, you would have the largest mass of gold if the chunk weighed 1 N on the Moon.