Final answer:
Bathroom scales measure weight and are calibrated to display mass based on Earth's gravitational acceleration. If external forces are applied or if the acceleration due to gravity changes, the display will not show the correct mass. In free fall, the scale reads zero since there is no net force acting on the springs within the scale. none of the option is correct.
Step-by-step explanation:
Bathroom scales are designed to measure the weight of an object, which is the force due to gravity acting on that object. The scale achieves this by using springs that compress proportionally to the force of weight they encounter. For a person with a mass m = 101.5 kg, the weight can be calculated using the acceleration due to gravity g = 9.80 m/s2, where weight W = m × g. The scale shows this weight but is typically calibrated to display the mass by dividing the weight measurement by the acceleration due to gravity. When the scale is on Earth and not accelerating, it shows the correct mass.
If you push down on a table while standing on a scale, the reading would increase, because you are adding more downward force through the scale. On the Moon, the scale would not show the same mass because the gravitational acceleration is different, so the person's weight would be less, thus affecting how the springs compress. Scales that are calibrated for Earth's gravity won't give a mass reading on the Moon without recalibration.
When standing on a scale in a free-falling elevator, the scale would not show any weight since both you and the scale are accelerating downwards at the same rate due to gravity, effectively simulating a state of weightlessness.