Answer:
B. You would weigh the same on both planets because their masses and the distance to their centers of gravity are the same.
Explanation:
Given that Planets A and B have the same size, mass.
Let the masses of the planets A and B are and
respectively.
As masses are equal, so .
Similarly, let the radii of the planets A and B are and
respectively.
As radii are equal, so .
Let my mass is m.
As the weight of any object on the planet is equal to the gravitational force exerted by the planet on the object.
So, my weight on planet A,
my weight of planet B,
By using equations (i) and (ii),
.
So, the weight on both planets is the same because their masses and the distance to their centers of gravity are the same.
Hence, option (B) is correct.