Final answer:
You are indeed lighter on the top of a skyscraper due to the weaker gravitational pull at higher altitudes, making the statement true. Engineers might consider this when designing skyscrapers, but the difference in weight is usually small. During free fall, such as in a snapped elevator cable scenario, you experience apparent weightlessness.
Step-by-step explanation:
The statement that you are lighter in weight when on the top level of a skyscraper compared to when you are on the bottom floor is true. Weight varies slightly with altitude due to changes in the gravitational force. The further you are from the center of the Earth, the weaker the gravitational pull, and thus you would weigh slightly less on the top of a skyscraper compared to the ground floor. This difference is very small and usually negligible for everyday purposes.
Engineers sometimes take into account the change in the value of 'g' when designing structural support for very tall buildings, although the change is typically very small and often can be ignored for practical engineering purposes. However, in precise applications or in structures of exceptional height, this factor might be considered for safety and structural integrity.
Similarly, when an elevator cable snaps, the scale would no longer show your real weight, but you would experience apparent weightlessness as both you and the scale free fall at the same acceleration due to gravity. This is different from your actual weight, which is the force exerted on you by gravity when you are in a non-accelerating frame of reference.