Final answer:
The acceleration due to gravity on Planet X must be calculated using the person's known mass and their weight on Planet X. None of the options provided match the correct calculation which is 19.6 m/s², indicating a possible error in the question.
option A is the correct
Step-by-step explanation:
To determine the acceleration due to gravity on Planet X, we can use the known relationship between weight and mass. Weight is the force due to gravity and is calculated by the formula w = mg, where w is weight, m is mass, and g is the acceleration due to gravity.
Since the person's weight on Earth is 1000 N, we can use the acceleration due to gravity on Earth (9.8 m/s²) to find their mass. Their mass would be 1000 N / 9.8 m/s² = 102.04 kg.
On Planet X, the person weighs 2000 N.
To find the acceleration due to gravity on Planet X, we keep the mass consistent and solve for g. The formula becomes 2000 N = 102.04 kg × g. Solving for g, we get g = 2000 N / 102.04 kg = 19.6 m/s². This value is not provided in the options, therefore the question might contain an error or additional information might be needed to answer correctly.