Final answer:
To calculate the weight of an object on a planet with double the Earth's mass and three times the radius, we consider the gravitational force changes. The weight on this new planet would be one-sixth of its weight on Earth, resulting in approximately 0.167 N, which is closest to option a. 0.167 N.
Step-by-step explanation:
The question is concerning the weight of an object in different gravitational fields. Weight is the force of gravity on an object and can be calculated by the equation w = mg, where w is weight, m is mass, and g is the acceleration due to gravity. On Earth, acceleration due to gravity is approximately 9.80 m/s².
To find the weight of an object on a different planet, we use the formula for gravitational force F = G(m1m2/r²), where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects (the radius of the planet in this case).
If the new planet has double the mass and triple the radius compared to Earth, the gravitational force, and therefore the weight of an object, will be affected. Since gravitational force is directly proportional to mass and inversely proportional to the square of the radius, you would expect the weight to be one-sixth of its weight on Earth, given that the planet's mass is double (2x effect) and the radius is triple (3² = 9x effect), assuming the object's mass remains constant.
Therefore, if an object weighs 1 N on Earth, its weight on the new planet would be 1 N / 6, which equals 0.167 N. However, since this option is not available in the multiple-choice answers and closest to option a. 0.167 N (rounded to 0.167 N).