Final answer:
If Earth's mass doubles with no change in its size, your weight will double. Weight is directly proportional to the mass of the object exerting gravitational force, in this case, the Earth. So the correct option is a.
Step-by-step explanation:
If Earth's mass somehow doubles with no change in its size, and your mass remains the same, your weight doubles. This is because weight is the force of gravity on an object, and it is directly proportional to the mass of the object causing the gravitational force. According to Newton's law of universal gravitation, the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In this scenario, since the Earth's mass doubles, the gravitational force, and thus your weight, would also double.
For example, doubling the mass of an object doubles its weight because the weight is two times the gravitational force between the object and Earth. If Earth had 10 times its present mass but the same volume, a person's weight would increase by a factor of 10 as well. Conversely, if Earth had only one-third its present mass, a person's weight would decrease by a factor of one-third. In the example of Earth increasing its volume by eight times, its radius would double, resulting in the gravitational force at the surface being reduced by a factor of ¼, so a person would weigh only one-fourth as much.