Final answer:
The force required to stop a block on a frictionless surface on the Moon is the same as on Earth because the property that determines the force needed is mass, not weight, and that doesn't change with location.
Step-by-step explanation:
To determine the force required to stop a block moving on a frictionless horizontal surface both on Earth and on the Moon, we must refer to Newton's laws of motion. The mass of the object and its velocity are the key factors in calculating the force needed to change its state of motion, according to Newton's second law which states that force equals mass times acceleration (F=ma). Gravity affects the object's weight but not its mass, and since there is no friction on the surface in both cases, gravity does not affect the stopping force required. Therefore, the force needed to stop the block within the same amount of time would be the same on the Moon as it is on Earth because it depends on the block's inertia, which remains unchanged between the two locations. Given that inertia and the necessary stopping time are constant, the block's mass and acceleration do not change, so the force required to stop the block on the Moon would be the same as on Earth. The correct option would be b. the force required would be the same.