Final answer:
A 100 kg man would have the least gravitational potential energy on the Moon when lifted to a height of 3 m because the Moon has the least gravitational pull compared to Earth, Mars, and Jupiter.
Step-by-step explanation:
A 100 kg man would have the least gravitational potential energy when lifted to a height of 3 m on Jupiter. Gravitational potential energy (GPE) is given by the formula GPE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height above the ground. Since 'm' and 'h' are held constant in this scenario, the only variable that affects GPE is 'g'. Jupiter has the highest gravity among the options provided, meaning that a person would weigh the most on its surface. However, this question is asking for where the man would have the least gravitational potential energy, which is counterintuitive if only considering weight. We should consider the gravitational potential energy formula more carefully, thus, the answer would be Earth, since it has greater acceleration due to gravity than the Moon or Mars, and the question asks where potential energy is the least for the same height, accounting for gravity's effect.
If we consider the other celestial bodies: on Mars and the Moon, the acceleration due to gravity is less than on Earth which suggests that the potential energy would be less because 'g' is smaller. However, since Jupiter has the strongest gravitational pull, a 100 kg man would weigh significantly more on Jupiter, increasing the 'g' value, and thus, his potential energy would also be much higher compared to the other bodies if he were lifted to the same height. Accounting for this, a man's gravitational potential energy would be least on the Moon, being the celestial body with the lowest gravitational pull of the options listed. Therefore, the correct option is B) Moon.