Final answer:
The acceleration due to gravity on Planet X is 19.6 m/s² since an object weighs twice as much there as it does on Earth, where gravity is 9.8 m/s².
The correct option from the provided choices would be (d) 19.6 m/s².
Step-by-step explanation:
The acceleration due to gravity on Planet X can be found by comparing the weights of an object on Earth and on Planet X. On Earth, where the acceleration due to gravity is 9.8 m/s², a 1.0 kg object has a weight of 9.8 N. Given that an object weighing 1000 N on Earth weighs 2000 N on Planet X, the acceleration due to gravity on Planet X can be found using the ratio of the weights (2000 N on Planet X / 1000 N on Earth), which is 2.
This means that gravity on Planet X is twice as strong as it is on Earth. Therefore, the acceleration due to gravity on Planet X would be 2 times 9.8 m/s², which equals 19.6 m/s². So the correct option from the provided choices would be (d) 19.6 m/s².